Question

Using the given pattern, find the missing numbers. 
\(1^ 2 + 2^2 + 2^2 = 3^2\)
\(2^ 2 + 3^2 + 6^2 = 7^2 \)
\(3^ 2 + 4^2 + 12^2 = 13^2 \)
\(4 ^2 + 5^2 + ....^2 = 21^2 \)
\(5^ 2 +....^2 + 30^2 = 31^2\) 
\(6^ 2 + 7^2 + ....^2 = ....^2\)

Answer 1

From the given pattern, it can be observed that,
(i) The third number is the product of the first two numbers.
(ii) The fourth number can be obtained by adding \(1\) to the third number.
Thus, the missing numbers in the pattern will be as follows.
\(4^2+5^2+\underline{20}^2=21^2\)
\(5^2+\underline6^2+30^2=31^2\)
\(6^2+7^2+\underline{42}^2=\underline{43}^2\)