What is the recursive formula for this geometric sequence?

-4, -24, -144, -864, ...

Solution:

Given that,

-4, -24, -144, -864

To find: recursive formula for geometric sequence

Find the common ratio "r"

The nth term of geometric sequence is given as:

Where,

n is the nth term

is the first term

r is the common ratio

From sequence,

Therefore,

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

Thus the recursive formula is found

The recursive formula is

Explanation:

The sequence is

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

Thus, we have,

Also,

And,

Hence, dividing each term of the sequence, the common ratio is

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

Substituting the value of r, we get,

Therefore, the recursive formula is