What is the common ratio of the geometric sequence below? -2, 4, -8, 16, -32, …

Solution:

Given, the geometric sequence is -2, 4, -8, 16, -32,....

We have to find the common ratio of the given geometric sequence.

In geometric sequence, a, b, c, d, … the common ratio r is given by

r = b/a = c/b = d/c.

So, r = 4/-2 = -8/4 = 16/-8 = -32/16 = -2

r = -2

Therefore, the common ratio is r = -2.

Example:

What is the common ratio of the geometric sequence below? 4, 16, 64, 256,...

Solution:

Given, the geometric sequence is 4, 16, 64, 256,...

We have to find the common ratio of the given geometric sequence.

In geometric sequence, a, b, c, d, … the common ratio r is given by

r = b/a = c/b = d/c.

So, r = 16/4 = 64/16 = 256/64 = 4

r = 4

Therefore, the common ratio is r = 4.

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What is the common ratio of the geometric sequence below? -2, 4, -8, 16, -32, …

Summary:

The common ratio of the geometric sequence -2, 4, -8, 16, -32,....is -2.