Question

If the third term is four times its fifth term, what are the possible values of the common ratio (r)?

a) r = 1/2
b) r = 2
c) r = 4
d) r = -2

Answer 1

The possible values of the common ratio (r) in a geometric sequence are 2 and -2.

Step-by-step explanation:

To find the common ratio (r) in a geometric sequence, we can set up an equation using the given information. Let's assume the third term is A and the fifth term is B. According to the problem, A = 4B. In a geometric sequence, each term is obtained by multiplying the previous term by the common ratio. So, we can write the equation as:

A = r2 × B

Substituting A = 4B, we get:

4B = r2 × B

Cancelling out B, we have:

4 = r2

Taking the square root of both sides, we get:

r = ± 2

So, the possible values for the common ratio (r) are 2 and -2. Therefore, the correct answer is option d) r = -2.