Question

Tell whether the sequence of y-values is arithmetic or geometric. Then, find y when n = 5.

A: arithmetic; When n = 5, y = 30.
B: arithmetic; When n = 5, y = 7776.
C: geometric; When n = 5, y = 7776.
D: geometric; When n = 5, y = 30.

Answer 1

C

Explanation:

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

Here the terms are 6, 36, 216, 1296

36 - 6 = 30

216 - 36 = 180

1296 - 216 = 1080

The difference between consecutive terms is not common.

Thus the sequence is NOT arithmetic

For a geometric sequence there is a common ratio r between consecutive terms.

`(36)/(6)` = 6

`(216)/(36)` = 6

`(1296)/(216)` = 6

there is a common ratio of r = 6 between consecutive terms

Thus the sequence is geometric

Each term in the sequence is obtained by multiplying the preceding term by r

then when n= 5 , y = 6 × (n = 4) = 6 × 1296 = 7776