Question

Observe the following pattern and find the missing numbers.

${11}^2=121$

${101}^2=10201$

${10101}^2=102030201$

${1010101}^2=\_\_\_\_\_\_\_$

$\_\_\_\_\_\_\_\_{\_}^2=10203040504030201$

Answer 1

From the given pattern, it can be observe that the number of $"1"$ is the middle term of the given digit followed by $0$ in both left and right side of that middle term.

Also, from middle term, numbers are decreasing in both side of middle term and again followed by $0$.

Also, the number starts and end with $1$.

${101}^2=10201$

Here the number of $"1"$ is $2$ which is exactly the middle term and to the left and right to the $2$ is $0$, followed by $1$.

Therefore,

${1010101}^2=1020304030201$

Similarly

For the number $102030405040302010$, it must contain five $1$.

$10203040504030201={101010101}^2$

Hence, the missing numbers are ${1010101}^2=1020304030201$ and $10203040504030201={101010101}^2$