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

Answer 2

Answer:

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

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.

Given the sequence:

-16, 4, -1, ...

This is a geometric sequence.

Here, $a_1 = -16$ and $r = -\frac{1}{4}$

Since,

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

$\frac{-1}{4} = -\frac{1}{4}$ ans so on .....

Substitute the given values we have;

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

⇒$a_n = -\frac{1}{4} \cdot a_{n-1}$

Therefore, the recursive formula for the following geometric sequence is, $a_n = -\frac{1}{4} \cdot a_{n-1}$