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8
0
GNisha
09/12/2025
Maths
Recurrance Relations
213
•
9 Dec 2025
•
GNisha
@gnisha_fhdqlrplxiup
Recurrence relations might sound complex, but they're actually just mathematical... Show more
Ever wondered how your savings grow with compound interest or how populations change over time? Recurrence relations are mathematical sequences where each term builds on the previous one, making them perfect for modelling real-world situations.
The basic form is , where each new term equals the previous term multiplied by a constant. Terms are labelled with being your starting value.
Quick Tip: When dealing with percentages, remember that keeping 96% means multiplying by 0.96, while gaining 4% means multiplying by 1.04.
For investment problems, if £2000 grows at 4% annually, your recurrence relation becomes . After three years, you'd have £2249.72 - not bad for understanding one simple pattern!
Things get more interesting with linear recurrence relations: . Now you're not just multiplying - you're adding a constant too, which opens up loads of practical applications.
Think about waste disposal: if 200 litres get dumped weekly but 30% naturally disappears, you get . The 0.7 represents the 70% that remains, whilst 200 is the weekly addition.
These relations are brilliant for modelling situations where something gets added regularly whilst a percentage is removed or lost. Your calculator becomes your best friend here - just keep pressing the equals button to see the pattern emerge.
Pro Tip: Always double-check your percentage calculations. If 30% is removed, then 70% remains, so multiply by 0.7, not 0.3!
Here's where it gets really clever - some sequences eventually settle down to a fixed value called a limit. For this to happen, you need in your relation .
To find the limit, use the formula or set and solve. This tells you the long-term behaviour without calculating hundreds of terms.
Back to that waste example: with , the limit is litres. If environmental regulations allow maximum 600 litres, the company gets rejected.
Remember: Always state whether a limit exists by checking if - examiners love seeing this!
Sometimes you'll get a sequence of numbers and need to find the recurrence relation that created them. This involves setting up simultaneous equations using consecutive terms.
Given , , and the form , you create two equations: and . Solving these gives and .
This reverse-engineering skill is incredibly valuable - you can spot patterns in real data and predict future behaviour. It's like being a mathematical detective!
Exam Strategy: When solving simultaneous equations, subtract one equation from the other to eliminate first - it's usually the quickest route.
Linked recurrence relations involve two connected sequences, often representing things moving between locations. These problems look scary but follow the same principles.
For car hire depots in Glasgow and Perth with 200 cars total, you track how cars move between locations based on return percentages. If Perth keeps 80% and Glasgow keeps 60%, you can model this as .
Since , substitute to get . The long-term distribution settles at 133 cars in Perth and 67 in Glasgow.
Key Insight: Always use the constraint that totals must add up correctly - it turns two variables into one manageable equation.
These problems appear complex but break down into familiar patterns once you identify the connections between sequences.
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
App Store
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
GNisha
@gnisha_fhdqlrplxiup
Recurrence relations might sound complex, but they're actually just mathematical patterns where each term depends on the previous one - think of them as sequences with a twist. You'll find these everywhere from calculating compound interest to predicting population changes,... Show more
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Ever wondered how your savings grow with compound interest or how populations change over time? Recurrence relations are mathematical sequences where each term builds on the previous one, making them perfect for modelling real-world situations.
The basic form is , where each new term equals the previous term multiplied by a constant. Terms are labelled with being your starting value.
Quick Tip: When dealing with percentages, remember that keeping 96% means multiplying by 0.96, while gaining 4% means multiplying by 1.04.
For investment problems, if £2000 grows at 4% annually, your recurrence relation becomes . After three years, you'd have £2249.72 - not bad for understanding one simple pattern!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Things get more interesting with linear recurrence relations: . Now you're not just multiplying - you're adding a constant too, which opens up loads of practical applications.
Think about waste disposal: if 200 litres get dumped weekly but 30% naturally disappears, you get . The 0.7 represents the 70% that remains, whilst 200 is the weekly addition.
These relations are brilliant for modelling situations where something gets added regularly whilst a percentage is removed or lost. Your calculator becomes your best friend here - just keep pressing the equals button to see the pattern emerge.
Pro Tip: Always double-check your percentage calculations. If 30% is removed, then 70% remains, so multiply by 0.7, not 0.3!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Here's where it gets really clever - some sequences eventually settle down to a fixed value called a limit. For this to happen, you need in your relation .
To find the limit, use the formula or set and solve. This tells you the long-term behaviour without calculating hundreds of terms.
Back to that waste example: with , the limit is litres. If environmental regulations allow maximum 600 litres, the company gets rejected.
Remember: Always state whether a limit exists by checking if - examiners love seeing this!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Sometimes you'll get a sequence of numbers and need to find the recurrence relation that created them. This involves setting up simultaneous equations using consecutive terms.
Given , , and the form , you create two equations: and . Solving these gives and .
This reverse-engineering skill is incredibly valuable - you can spot patterns in real data and predict future behaviour. It's like being a mathematical detective!
Exam Strategy: When solving simultaneous equations, subtract one equation from the other to eliminate first - it's usually the quickest route.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Linked recurrence relations involve two connected sequences, often representing things moving between locations. These problems look scary but follow the same principles.
For car hire depots in Glasgow and Perth with 200 cars total, you track how cars move between locations based on return percentages. If Perth keeps 80% and Glasgow keeps 60%, you can model this as .
Since , substitute to get . The long-term distribution settles at 133 cars in Perth and 67 in Glasgow.
Key Insight: Always use the constraint that totals must add up correctly - it turns two variables into one manageable equation.
These problems appear complex but break down into familiar patterns once you identify the connections between sequences.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
8
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
App Store
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Sociology