Question

What is the recursive formula for this geometric sequence? -4, -24, -144, -864, ...

Answer 1

The recursive formula is $a_n=6(a_{n-1})$

Explanation:

The sequence is $-4,-24,-144,-864, \dots$

Since, it is given that it is a geometric sequence, let us find the common ratio of the sequence.

Thus, we have,

$r=\frac{-24}{-4} =6$

Also,

$r=\frac{-144}{-24} =6$

And,

$r=\frac{-864}{-144} =6$

Hence, dividing each term of the sequence, the common ratio is $r=2$

Now, we shall determine the recursive formula for this geometric sequence.

The formula to find the recursive formula for the geometric sequence is given by

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

Substituting the value of r, we get,

$a_n=6(a_{n-1})$

Therefore, the recursive formula is $a_n=6(a_{n-1})$

Answer 2

The recursive formula for this geometric sequence is:

$a_n = -4 \times 6^{n-1}$

Solution:

Given that,

-4, -24, -144, -864

To find: recursive formula for geometric sequence

Find the common ratio "r"

$r = \frac{-24}{-4} = 6\\\\ r = \frac{-144}{-24} = 6$

The nth term of geometric sequence is given as:

$a_n = a_1 \times r^{n-1}$

Where,

n is the nth term

$a_1$ is the first term

r is the common ratio

From sequence,

$a_1 = -4\\\\r = 6$

Therefore,

$a_n = -4 \times 6^{n-1}$

Where, n = 1, 2, 3, ....

Thus the recursive formula is found