# What are the numbers that come next in these sequences: 3,9,27,81?

Feb 15, 2016

The 5th term:$= 243$

#### Explanation:

$3 , 9 , 27 , 81$

The above sequence is identified as a geometric sequence because a common ratio is maintained throughout the sequence.

The common ratio $\left(r\right)$ is obtained by dividing a term by its preceding term:

1) r = 9/3 =color(blue)(3

We need to find the fifth term of the sequence:

The 5th term can be obtained through formula:

${T}_{n} = a {r}^{n - 1}$

(note: $a$ denotes the first term of the series)
$a = 3$

${T}_{5} = 3 \times {3}^{\left(5 - 1\right)}$

$= 3 \times {3}^{4}$

$= 3 \times 81$

$= 243$