Question

What is the next number in the pattern: $4,9,16,25?$

Answer 1

Hint: As we can see that there is a pattern of the numbers. Number pattern is a pattern or sequence in a series of numbers. This pattern generally establishes a common relationship between all numbers. In this question we have to find that pattern that binds them all and then apply on them and then we find the next number on the basis of it.

Complete step by step solution:
We have been given a pattern here $4,9,16,25$.
We can see that all these given numbers are the perfect squares. The numbers can be written as $4 = {2^2},9 = {3^2},16 = {4^2}$ and $25 = {5^2}$. So the numbers are consecutive and the next number is $6$.
Therefore we can write them as ${2^2},{3^2},{4^2},{5^2},{6^2}$ . So the numbers are $4,9,16,25,36$.
Hence the required next number is $36$.

Note:
In this kind of question we should always try to first find the pattern between the numbers. There are several patterns as there can be difference between the numbers as see in Arithmetic progression, there can be perfect cube of the numbers. As for example the series of numbers $8,27,64,125...$. These are the perfect cubes i.e. ${2^3},{3^3},{4^3},{5^3}$, so we can say that the next number in the pattern is ${6^3} = 216$.