Question

Observe the following pattern and fill in the missing number.
${11^2} = 121$
${101^2} = 10201$
${10101^2} = 102030201$
${1010101^2} = ..............$

Answer 1

Hint:In the given question, we have to analyze the pattern in the squares of the given numbers and then predict the next number in the sequence following the same pattern. The pattern that we analyze in the question can also be verified by actually calculating the square of the terms.

Complete step by step answer:
So, we are given a series of the squares of some numbers as:
${11^2} = 121$
${101^2} = 10201$
${10101^2} = 102030201$
Now, we have to analyze the pattern in the squares of the numbers given to us in the question itself.
Now, we have the square of $11$ as $121$.
Square of $101$ as $10201$
Square of $101$ is similar to square of $11$ as we have inserted zero between all the digits in the square of $11$ to obtain the square of $101$.
Also, Square of $10101$ as $102030201$
Square of $10101$ is similar to the square of $101$ as we have introduced the next number $3$ in the sequence in the square of $101$ to obtain the square of $10101$.
Similarly, going with the pattern that we have analyzed in the previous cases, we can predict the square of $1010101$.
Therefore, the square of $1010101$ would also be similar to the square of $1010101$ as we have to introduce the next number $4$ in the sequence in the square of $10101$ to obtain the square of $1010101$.
So, following the pattern, we get the square of $1010101$ as $1020304030201$.

Note: We can verify the answer of the missing number or term by actually calculating the square of the number $1010101$. There are many such patterns that can be observed so as to do calculations quicker and accurately.