Finding the Nth Term of Linear Sequences
Every linear sequence follows a simple pattern where you add (or subtract) the same number each time. Your job is to spot this pattern and turn it into a formula.
The nth term formula always follows the same structure: an + b, where 'a' is how much you're adding each time, and 'b' adjusts for where the sequence actually starts. Think of it like a recipe - once you know the ingredients, you can make any term you want!
Let's break down the example: -3, -1, 1, 3, 5, 7... Notice each term goes up by +2, so we know the first part is 2n. But here's the clever bit - the sequence starts at -3, not +2 (what 2×1 would give us). Since -3 is 5 less than +2, we subtract 5 to get our final formula: nth term = 2n - 5.
Quick Check: Test your formula by plugging in n=1. Does 2(1)-5 = -3? Perfect! Your formula works.