64, -48, 36, -27 which formula can be used to describe the sequence

A sequence is either arithmetic or geometric. The given sequence is geometric and the formula is

First, we determine if the sequence is arithmetic or geometric.

An arithmetic sequence has a common difference (d) and it is calculated as follows:

or

So, we have:

The 2 values of d are not equal; So, the sequence is not arithmetic.

Next, we check if it is geometric.

A geometric sequence has a common ratio (r) and it is calculated as follows:

or

So, we have:

The 2 values of r are equal; So, the sequence is geometric.

The formula of a geometric sequence is:

Where:

--- the first term

--- the common ratio

So, we have:

Apply law of indices

Rewrite as:

Apply reciprocals

Hence, the formula to describe the sequence is:

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 Formula      Multiply the number by  -3/4

The number 48 is 3/4 of 64 but it is negative so the result of -48 should be multiplying 64 by negative 3/4

64x-3/4 =-48

after 48 will be a positive number since (-)x(-)=(+)

So it will be alternating positive and negative