Question

Tell whether the given sequence of y-values is arithmetic or geometric. Identify a function that describes the sequence, and then find y when n = 5.ㅤ−7, −6, −5, −4, ...

ㅤ
A: geometric; y = 2n + 1; 11

B: geometric; y = 3n; 15

C: arithmetic; y = n + 1; 6

D: arithmetic; y = n − 8; −3

Answer 1

D

Explanation:

An arithmetic sequence has a common difference d between consecutive terms.

the terms are - 7, - 6, - 5, - 4

- 6 - (- 7) = - 6 + 7 = 1

- 5 - (- 6) = - 5 + 6 = 1

- 4 - (- 5) = - 4 + 5 = 1

there is a common difference of d = 1

Thus the sequence is arithmetic

the nth term of an arithmetic sequence is

`a_(n)` = a₁ + d(n - 1)

where a₁ is the first term and d the common difference

here a₁ = - 7 , d = 1 and
`a_(n)` = y , then

y = - 7 + 1(n - 1) = - 7 + n - 1 = n - 8

when n = 5 , then

y = 5 - 8 = - 3

D : arithmetic : y = n - 8 : - 3