Question
Observe the following patterns and supply the missing numbers
$\begin{aligned} 11^2 & =121 \\ 101^2 & =10201 \\ 10101^2 & =102030201 \\ 1010101^2 & =\ldots . . . . . . . . .. . . .\\ .........&{ }^2=10203040504030201\end{aligned}$

Answer

According to the first three patterns, we see that given numbers are in odd digits. When we square the given number, we get the number in the odd position. Starting from 1 and consecutive increasing number upto the number of odd digits in the given number and then consecutive decreasing number upto 1 and all the even position number 0 exist.
(i) $1010101^2=1020304030201$
(ii) $101010101^2=10203040504030201$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free