Find a formula for the nth term of the arithmetic sequence.

Question

Answer 1

a_n = a₁ + d(n-1)

a_n = 22 + 2(n-1) = 22 + 2n-2 = 2n+20

Answer 2

Hi Xavier,

Suppose you don't remember the formula but realize that an arithmetic sequence increases or decreases in a linear fashion. A table can easily be constructed:

Term Value

0 20

1 22

2 24

3 26

You can see there is a starting value of 20 at term 0, and an increase of 2 for each new term. Applying an equation you probably remember much better, y = mx + b, you can write a_n = 2n + 20

Enjoy