Question

Using the given pattern, find the missing numbers.
$1^2+2^2+2^2=3^2$
$2^2+3^2+6^2=7^2$
$3^2+4^2+{12}^2={13}^2$
$4^2+5^2+{20}^2={21}^2$
$5^2+6^2+{30}^2={31}^2$
$6^2+7^2+{42}^2=..{.}^2$

Answer 1

$1^2+2^2+2^2=3^2$
$2^2+3^2+6^2=7^2$
$3^2+4^2+{12}^2={13}^2$
$4^2+5^2+..{.}^2={21}^2$
$5^2+..{.}^2+{30}^2={31}^2$
$6^2+7^2+..{.}^2=..{.}^2$
Or
$1^2+2^2+(1\times 2{)}^2=(1\times 2+1{)}^2$
$2^2+3^2+(2\times 3{)}^2=(2\times 3+1{)}^2$
$3^2+4^2+(3\times 4{)}^2=(3\times 4+1{)}^2$
$4^2+5^2+(4\times 5{)}^2=(4\times 5+1{)}^2$
$5^2+6^2+(5\times 6{)}^2=(5\times 6+1{)}^2$
$6^2+7^2+(6\times 7{)}^2=(6\times 7+1{)}^2$

$\therefore$ misssing number is $(6\times 7+1)=43$