Question

Formulate the recursive formula for the following geometric sequence.

{-16, 4, -1, ...}

Answer that question with all work shown. Thanks

Answer 1

a_n=-\frac{1}{4 a_{n-1}

Explanation:

The recursive formula for the geometric sequence is given by:

a_n = a_{n-1} \cdot r

where,

r is the common ratio terms

-16, 4, -1, ...

This is a geometric sequence.

Here, and

Since,

ans so on .....

Substitute the given values we have;

⇒

Therefore, the recursive formula for the following geometric sequence is,

Answer 2

`A_n= A_(n-1) ((-1)/(4))`

Explanation:

Formulate the recursive formula for the following geometric sequence.

{-16, 4, -1, ...}

Here the common difference of two terms are not same.

LEts find the common ratio. To find common ratio, divide the second term by first term

`(4)/(-16) =(-1)/(4)`

`(-1)/(4) =(-1)/(4)`

So common ratio is -1/4

Recursive formula is

`A_n= A_(n-1) (r)`

'r' is the common ratio.

Recursive formula becomes

`A_n= A_(n-1) ((-1)/(4))`