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

$1^2+2^2+2^2=3^2$

$2^2+3^2+6^2=7^2$

$3^2+4^2+{12}^2={13}^2$

$4^2+5^2+{20}^2={21}^2$

$5^2+6^2+{30}^2={31}^2$

$6^2+7^2+{42}^2={43}^2$

We got $20$ because $2\ast 3=6,3\ast 4=12$, similarly, $4\ast 5=20$

we got $6$ because $2\ast 3=6,3\ast 4=12,4\ast 5=20$ similarly, $5\ast 6=30$

we got $42$ because $2\ast 3=6,3\ast 4=12,4\ast 5=20,5\ast 6=30$ similarly , $6\ast 7=42$

we got $43$ because the answer is the number after the last number in the question

As, after $2$ it is $3$, after $6$ it is $7$, after $12$ it is $13$, similarly, after $42$ it is $43$.