Question

What is the next number in the sequence $\underline {} ,\,\underline {} ,\,16,\,25,\,36$?

Answer 1

In this question, we have to consider the first and second blank as the place of the first and second number. Then we have to identify the pattern which is following in the above question
and then according to that pattern we have to find the next term of $36$.The pattern would be ${x_n} = {\left( {n + 1} \right)^2}$, where ${x_n}$ is the number of terms to be found and ${\left( {n + 1} \right)^2}$ is the term we have to find.

Complete step-by-step answer:
In the above question, we have given a particular sequence and we have to find the term after $36$.
Here, the first two blanks represent the first two terms and the third, fourth and fifth terms are $16,\,25\,and\,36$ respectively.
So, we have to find the ${6^{th}}$ term of the above sequence.
Here we can notice that
$16 = {\left( 4 \right)^2}$
$25 = {\left( 5 \right)^2}$
$36 = {\left( 6 \right)^2}$
So, the third term is a perfect square of $4$ and the fourth term is a perfect square of $5$ and so on.
Therefore, we can identify the pattern here as ${x_n} = {\left( {n + 1} \right)^2}$, where ${x_n}$ is that term which we have to find and n is the number of that term.
Here, we have to find the ${6^{th}}$ term, so the value of n is $6$here which we have to put in the formula ${x_n} = {\left( {n + 1} \right)^2}$.
On putting the value of n in the above pattern, we get
${x_6} = {\left( {6 + 1} \right)^2}$
$\Rightarrow {\left( 7 \right)^2}$
$\Rightarrow 49$

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.