Question

Choose the explicit and recursive formulas for the geometric sequence 45, 135, 405, 1215, 3645, .... PLEASE HELP ASAP

Answer 1

Option (B)

Explanation:

Given sequence is 45, 135, 405, 1215, 3645..........

Since it's a geometric sequence,

Common ratio of each successive term to the previous term

r =
`(135)/(45)=3`

First term of the sequence 'a' = 45

Explicit formula of a geometric sequence will be,

`a_n=a(r)^(n-1)`

`a_n=45(3)^(n-1)`

Recursive formula of this sequence will be,

`a_n=3(a_(n-1))`,
`a_1=45`

Therefore, Option (B) will be the answer.