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.
$4^2+5^2+\underline{20}^2=21^2$
$5^2+\underline6^2+30^2=31^2$
$6^2+7^2+\underline{42}^2=\underline{43}^2$