Question

Find the pattern 2,3,4,9,8,27,16

Answer 1

Hey mate,

The pattern here is

a, b, a×a, b×b, a×a×a, b×b×b, a×a×a×a, b×b×b×b

or

nth term of this series is:

{ 2^((n+1)/2) , if n is odd number

3^(n/2) , if n is even number.

hope this helps you out!

Answer 2

The pattern is to be continued as 2,3,4,9,8,27,16,81,32.......

Given:

The given pattern is 2,3,4,9,8,27,16

To Find:

We need to find how this pattern is obtained and continue the pattern

Solution:

Let us solve this problem very simply.

As we observe the pattern the odd terms are even and they are in powers of 2. The even terms look like a multiple of 3 which are the powers of 3.

It can  be mathematically expressed as

$=2^{\frac{n+1}{2} } \ for\ odd\ terms\\\\=3^{\frac{n}{2} }\ for \ even \ terms$

where the value of n starts from 1. If n is odd we will go with the first mathematical expression, If n is even we will go with the second expression.

The remaining terms in the sequence would be 81,32.......

Therefore the logic behind the sequence is $2^{1}, 3^{1}, 2^{2}, 3^{2}, 2^{3}, 3^{3}$ and the next two terms would be 81, 32.

#SPJ2