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# Find the common ratio of the sequence. -164, -82, -41, -20.5, . . .

**Solution:**

Given sequence is -164, -82, -41, -20.5, . . .

Common ratio = t_{2 }/ t_{1} = -82 / -164 = 1 / 2

Also t_{3 }/ t_{2} = -41 / -82 = 1/2

The ratio 1 / 2 is the same in the sequence, hence called the common ratio.

In general if a_{1}, a_{2}, a_{3}, a_{4},...,a_{n} are n terms of geometric progression then,

Common ratio, r = a_{n} /a_{n - 1} where, a_{n} is the n^{th} term of the geometric progression and a_{n - 1} is the (n - 1)^{th} term of the geometric progression.

## Find the common ratio of the sequence. -164, -82, -41, -20.5, . . .

**Summary:**

The common ratio of the sequence -164, -82, -41, -20.5, . . . is 1/2.

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