Question

Given the sequence 7, 12, 17, 22, ...

Which expression can be used to find the nth term in the sequence?
A. 2n +5
B. 3n+4
OC. 4n+3
D. 5n +2

Answer 1

option D is true.

Explanation:

Given the sequence

7, 12, 17, 22, ...

An arithmetic sequence has a constant difference 'd' and is defined by

`a_n=a_1+\left(n-1\right)d`

Computing the differences of all the adjacent terms

`12-7=5,\:\quad \:17-12=5,\:\quad \:22-17=5`

The difference between all the adjacent terms is the same

so

`d=5`

as

`a_1=7`

Thus, the nth term of the arithmetic sequence will be:

`a_n=5\left(n-1\right)+7`

`a_n=5n+2`

Therefore, option D is true.