Recursive formula for this geometric sequence, -125, -25, -5, -1

Recursive formula for this geometric sequence, -125, -25, -5, -1 will be:

 where  

Step-by-step explanation:

As we know that when we define a sequence by describing the relationship between its successive terms, it means we are defining the sequence recursively.

Given that,

-125, -25, -5, -1

As the recursive formula makes us able to find the next term in the sequence from the proceeding term by multiplying the preceding term by r.

Therefore,

Recursive formula for this geometric sequence, -125, -25, -5, -1 will be:

 where  

Step-by-step explanation:

The given geometric sequence is:

-125, -25, -5, -1

We want to find a recursive formula for the given geometric sequence.

The first term of this sequence is

The common ratio is

The recursive definition is given by:

We substitute the ratio to get: