Question

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Answer 1

The recursive formula for the geometric sequence is $a_n=(-\frac{1}{4} )a_{n-1}$

Explanation:

The given sequence is $\{-16,4,-1,........\}$

We need to determine the recursive formula for the given geometric sequence.

To determine the recursive formula, first we shall find the common difference.

Since, it is a geometric sequence, the common difference can be determined by

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

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

Hence, the common difference of the given geometric sequence is $r=-\frac{1}{4}$

The recursive equation for the geometric sequence can be determined using the formula,

$a_n=r(a_{n-1})$

Substituting the value $r=-\frac{1}{4}$, we get,

$a_n=(-\frac{1}{4} )a_{n-1}$

Thus, the recursive formula for the geometric sequence is $a_n=(-\frac{1}{4} )a_{n-1}$