Question

Given the sequence 3, 1,-1, -3, ... use the arithmetic sequence formula to write an equation.

Then, find a32.

Answer 1

a₃₂ = - 59

Explanation:

The nth term of an arithmetic sequence is

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 3 and d = a₂ - a₁ = 1 - 3 = - 2 , then

`a_(n)` = 3 - 2(n - 1) = 3 - 2n + 2 = - 2n + 5

Then

a₃₂ = - 2(32) + 5 = - 64 + 5 = - 59