What should be the next number in the following series? 3, 9, 27, 81, 243,…?

Solution:

Given, the series 3, 9, 27, 81, 243,... is in geometric progression.

First term, a = 3

Common ratio, r = 9/3 = 27/9 = 81/27 = 243/81

= 3

We have to find the next number in the series.

The n-th term of a geometric sequence is given by \(a_{n}=ar^{(n-1)}\)

Here, the next number implies the 6th term of the series.

So, \(a_{6}=3(3)^{(6-1)}\)

\(a_{6}=3(3)^{5}\)

\(a_{6}=(3)^{6}\)

\(a_{6}=729\)

Therefore, the next number in the series is 729.

What should be the next number in the following series? 3, 9, 27, 81, 243,…?

Summary:

The next number in the following series 3, 9, 27, 81, 243,.. should be 729.