Question

If the sixth term in a geometric sequence is 1/625, and the common ratio is 15, find the explicit formula of the sequence.

A. an=(15)n−1 for n ≥ 1
B. an=(5)⋅(15)n−1 for n ≥ 2
C. an=(5)⋅(15)n−1 for n ≥ 1
D. an=(1)⋅(15)n−1 for n ≥ 2

Answer 1

Answer :)

C is the answer... so yea ★

Answer 2

The explicit formula of the sequence is
`a_n=5((1)/(5))^(n-1)` for
`n \geq 2`

Explanation:

Sixth term in a geometric sequence =
`(1)/(625)`

Common ratio =
`(1)/(5)`

Formula of nth term =
`a_n=ar^(n-1)`

Substitute the values

So,
`(1)/(625)=a((1)/(5))^(6-1)\\(1)/(625)=a((1)/(5))^(5)\\(1)/(625) * 5^5=a`

5=a

Substitute the value in 1

So,
`a_n=5((1)/(5))^(n-1)`

So, Option C is true

Hence the explicit formula of the sequence is
`a_n=5((1)/(5))^(n-1)` for
`n \geq 2`