If 2, a, b, −54 forms a geometric sequence, find the values of a and b.

The values are a=-6 and b=18.

Step-by-step explanation:

A Geometric sequence is given by the formula   for all , where r ≠ 0 is the common ratio and is the first term of the sequence .

In this problem we know that m= 2, is the second term of the sequence and   is the third term.

First we need to find the general form of the sequence, we can use the fourth term and the value of to find r.

We replace   and   in the formula  , then we have

.

Therefore the general form of the sequence is   for all .

To find the value of a, we replace n=2 in our formula, so

.

To find the value of b, we replace n=3 in our formula, so

.

the answer is a

step-by-step explanation: