Question

Is the following sequence a geometric sequence? If so, find its common ratio. 6,24,96,384,1536,…

Answer 1

The given sequence is a geometric sequence and the common ratio is 4

Explanation:

A geometric sequence is a sequence in which the next term is obtained by multiplying the previous term with a ratio r.

Given sequence is:

6,24,96,384,1536,…

Here

a1 = 6

a2 = 24

a3 = 96

a4 = 384

a5 = 1536

The common ratio is the ratio between consecutive terms of a geometric sequence.

If the common ratio of a sequence is same, then the sequence is a geometric sequence.

So,

`r = (a_2)/(a_1) = (24)/(6) = 4\\r = (a_3)/(a_2) = (96)/(24) = 4\\r = (a_4)/(a_3) = (384)/(96) = 4\\r = (a_5)/(a_4) = (1536)/(384)= 4`

As the common ratio is same, the given sequence is a geometric sequence.

Hence,

The given sequence is a geometric sequence and the common ratio is 4