Question

Formulate the recursive formula for the following geometric sequence. {-16, 4, -1, ...}

Answer 1

each term is negative and 1/4 of previous term
so the nth term is the n-1 term times -1/4

so

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

Answer 2

`a_n=-(1)/(4) \cdot 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.

Given the sequence:

-16, 4, -1, ...

This is a geometric sequence.

Here,
`a_1 = -16` and
`r = -(1)/(4)`

Since,

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

`(-1)/(4) = -(1)/(4)` ans so on .....

Substitute the given values we have;

`a_n = a_(n-1) \cdot -(1)/(4) = -(1)/(4) \cdot a_(n-1)`

⇒
`a_n = -(1)/(4) \cdot a_(n-1)`

Therefore, the recursive formula for the following geometric sequence is,
`a_n = -(1)/(4) \cdot a_(n-1)`