Question

Formulate the recursive formula for the following geometric sequence.

Answer 1

Answer:

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

Step-by-step 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

Answer:

$A_n= A_{n-1} (\frac{-1}{4})$

Step-by-step 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

$\frac{4}{-16} =\frac{-1}{4}$

$\frac{-1}{4} =\frac{-1}{4}$

So common ratio is -1/4

Recursive formula is

$A_n= A_{n-1} (r)$

'r' is the common ratio.

Recursive formula becomes

$A_n= A_{n-1} (\frac{-1}{4})$