Geometric sequences and series are fundamental concepts in maths where...
Maths131 views·Updated 9 Sept 2026·2 pagesMastering Geometric Sequences: A Level Revision Guide
Neil Trivedi - MyEdSpace@neildoesmaths
1
of 2
Geometric Sequences
Ever wondered how population growth or compound interest actually works mathematically? Geometric sequences are the answer - they're sequences where you multiply by the same number (called the common ratio) to get from one term to the next.
The formula for the nth term is straightforward: , where 'a' is your first term and 'r' is your common ratio. Don't get caught up overthinking the bit - if you need the 5th term, just work out directly.
When you're given two terms and need to find 'a' and 'r', set up equations for both terms then divide one by the other. This clever trick eliminates 'a' and gives you 'r' straight away, then you can substitute back to find 'a'.
Quick tip: Always check your common ratio makes sense - if the sequence is decreasing, your ratio should be between 0 and 1!
2
of 2
Geometric Series
Now things get more interesting - what happens when you add up all those terms? A geometric series is simply the sum of a geometric sequence, and there's a brilliant formula that saves you from adding dozens of terms manually.
The sum formula comes from a clever algebraic trick. You write out the sum, multiply everything by 'r', then subtract to cancel out most terms - leaving just the first and last bits.
The alternative form is exactly the same formula rearranged. Use whichever version feels more comfortable, but remember you can't use either when (that would make the denominator zero!).
Exam hint: Always find your common ratio first by dividing consecutive terms - this prevents careless errors in longer calculations.
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Maths131 views·Updated 9 Sept 2026·2 pagesMastering Geometric Sequences: A Level Revision Guide
Neil Trivedi - MyEdSpace@neildoesmaths
Geometric sequences and series are fundamental concepts in maths where each term relates to the previous one through multiplication by a constant ratio. Understanding how to find terms and calculate sums will help you tackle A-level questions with confidence.
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Geometric Sequences
Ever wondered how population growth or compound interest actually works mathematically? Geometric sequences are the answer - they're sequences where you multiply by the same number (called the common ratio) to get from one term to the next.
The formula for the nth term is straightforward: , where 'a' is your first term and 'r' is your common ratio. Don't get caught up overthinking the bit - if you need the 5th term, just work out directly.
When you're given two terms and need to find 'a' and 'r', set up equations for both terms then divide one by the other. This clever trick eliminates 'a' and gives you 'r' straight away, then you can substitute back to find 'a'.
Quick tip: Always check your common ratio makes sense - if the sequence is decreasing, your ratio should be between 0 and 1!
2
of 2Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Geometric Series
Now things get more interesting - what happens when you add up all those terms? A geometric series is simply the sum of a geometric sequence, and there's a brilliant formula that saves you from adding dozens of terms manually.
The sum formula comes from a clever algebraic trick. You write out the sum, multiply everything by 'r', then subtract to cancel out most terms - leaving just the first and last bits.
The alternative form is exactly the same formula rearranged. Use whichever version feels more comfortable, but remember you can't use either when (that would make the denominator zero!).
Exam hint: Always find your common ratio first by dividing consecutive terms - this prevents careless errors in longer calculations.
We thought you’d never ask...
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