Question

What is the 20th number in the sequence $1,4,9,16,25,36$?

Answer 1

To find the missing term in a sequence, find the logic behind the sequence. In the given sequence $1,4,9,16,25,36$, observe that all the terms are squares. So, here the pattern would be ${x_n} = {n^2}$, where ${x_n}$ is the number of terms to be found and ${n^2}$ is the term we have to find. So, the 20th term would be ${x_{20}}$.

Complete step by step solution:
In this question, we are given a sequence $1,4,9,16,25,36$ and we have to find what will be the 20th term of this sequence.
First of all, what is a sequence?
A sequence is a set of numbers that are ordered.
For example: $2,4,6,8...$
This is a sequence of even numbers and the next term will be 10.
Each number in the sequence is called a term.
Now, to find a missing term in the sequence, first find a pattern behind the series.
Like in the above example, we were given a sequence of even numbers, so we could figure out the next term based on that pattern.
But, in our question, we are given a sequence of squares.
$\Rightarrow 1,4,9,16,25,36 = {1^2},{2^2},{3^2},{4^2},{5^2},{6^2}$
Observe that here, the pattern is ${x_n} = {n^2}$.
Where ${x_n}$ is the number of the term and ${n^2}$ is the term.
So, if we want to find the 1st term, put $n = 1$.
$\Rightarrow {x_1} = {\left( 1 \right)^2} = 1$
But, we have to find the 20th term. So, put $n = 20$.
$\Rightarrow {x_{20}} = {\left( {20} \right)^2} = 400$
Therefore, the 20th term in the sequence $1,4,9,16,25,36$ will be $400$.

Note:
This is a logic based question and there can be multiple patterns behind this sequence. So, there may be more than one correct answer to this question. For example: Another pattern for this sequence is that the difference between two consecutive terms is an odd number.