The first term of a geometric sequence is 15, and the 5th term of the sequence is

What are the geometric means between these terms?

Enter your answer by filling in the boxes to correctly complete the geometric sequence. Enter any fractions as simplified fractions.

15, __, __, __,

The geometric sequence is

Explanation:

Given that the first term of the geometric sequence is 15

The fifth term of the sequence is

We need to find the 2nd, 3rd and 4th term of the geometric sequence.

To find these terms, we need to know the common difference.

The common difference can be determined using the formula,

where and

For , we have,

Simplifying, we have,

Thus, the common difference is

Now, we shall find the 2nd, 3rd and 4th terms by substituting in the formula

For

Thus, the 2nd term of the sequence is 9

For , we have,

Thus, the 3rd term of the sequence is

For , we have,

Thus, the 4th term of the sequence is

Therefore, the geometric sequence is

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step-by-step explanation: