Question

Find an equation for the nth term of the arithmetic sequence.

-17, -12, -7, -2, ...

A. an = -17 + 5(n + 2)
B. an = -17 + 5(n + 1)
C. an = -17 + 5(n - 1)
D. an = -17 x 5(n - 1)

Answer 1

Option C
`a_n=-17+5(n-1)`

Explanation:

we know that

In an Arithmetic Sequence the difference between one term and the next is a constant, and this constant is called the common difference

The formula of the nth term of the arithmetic sequence is

`a_n=a_1+d(n-1)`

where

`a_n` is the nth term

`a_1` is the first term

d is the common difference

n is the number of terms

In this problem we have

`a_1=-17`

`a_2=-12`

`a_3=-7`

`a_4=-2`

Find the common difference d

`a_2-a_1=-12-(-17)=5`

`a_3-a_2=-7-(-12)=5`

`a_4-a_3=-2-(-7)=5`

The common difference is d=5

substitute the values in the formula

`a_n=-17+5(n-1)`