Question

A sequence is shown below. 45, 38, 31, 24, 17, ... Which function defines the nth term of the sequence?

Answer 1

f(n) = 52 - 7n

Explanation:

there is a common difference between consecutive terms in the sequence, that is

38 - 45 = 31 - 38 = 24 - 31 = 17 - 24 = - 7

This indicates the sequence is arithmetic with nth term

`a_(n)` = a₁ + d(n - 1)

a₁ is the first term, d the common difference, n the term number

here a₁ = 45 and d = - 7 , then

`a_(n)` = 45 - 7(n - 1) = 45 - 7n + 7 = 52 - 7n

the function defining the sequence is

f(n) = 52 - 7n