Question

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

Answer 1

The third number which is squared in the pattern $=$ product of the first two numbers which are squared.
The answer is the square of the next number of this product number.

So,
$4^2+5^2+{20}^2={21}^2$
$5^2+6^2+{30}^2={31}^2$
$6^2+7^2+{42}^2={43}^2$