Question

What are the first three terms of a geometric sequence in which a5=25 and the common ratio is 5?

Answer 1

Answer: A: 1/25, 1/5, 1

Explanation:

Answer 2

The first term is 0.04.

The second term is 0.2.

The third term is 1.

Explanation:

In a geometric sequence, we have that:

`a_(n+1) = r*a_(n)`.

In which r is the common ratio.

In this problem, we have that:

`a_(5) = 25` and
`r = 5`. So:

`a_(n+1) = r*a_(n)`.

`a_(5) = 5*a_(4)`

`25 = 5a_(4)`

`a_(4) = 5`

--------

`a_(4) = 5*a_(3)`

`5 = 5a_(3)`

`a_(3) = 1`

The third term is 1.

--------

`a_(3) = 5*a_(2)`

`1 = 5a_(2)`

`a_(2) = 0.2`

The second term is 0.2.

--------

`a_(2) = 5*a_(1)`

`0.2 = 5a_(1)`

`a_(1) = 0.04`

The first term is 0.04.