Question

Need help geometric sequences see pic for details

Answer 1

Given:

The recursive formula of a geometric sequence is

`a_n=a_(n-1)\cdot ((1)/(8))`

`a_1=-3`

To find:

The explicit formula of the given geometric sequence.

Solution:

We know that, first term of geometric sequence is
`a_1=-3`.

Recursive formula of a geometric sequence is

`a_n=a_(n-1)* r` ...(i)

where, r is common ratio.

We have,

`a_n=a_(n-1)\cdot ((1)/(8))` ...(ii)

On comparing (i) and (ii), we get

`r=(1)/(8)`

The explicit formula of a geometric sequence is

`a_n=a_1r^(n-1)`

Putting
`a_1=-3` and
`r=(1)/(8)`, we get

`a_n=-3\left((1)/(8)\right)^(n-1)`

Therefore, the correct option is D.