Which of the following triplets are Pythagorean?

$(10, 24, 26)$

Which of the following triplets are Pythagorean?

$(16, 63, 65)$

Which of the following triplets are Pythagorean?

$(12, 35, 38)$

Observe the following pattern

$(1\times 2)+(2\times 3)=\frac{2\times 3\times 4}{3}$

$(1\times 2)+(2\times 3)+(3\times 4)=\frac{3\times 4\times 5}{3}$

$(1\times 2)+(2\times 3)+(3\times 4)+(4\times 5)=\frac{4\times 5\times 6}{3}$

and find the value of

$(1\times 2)+(2\times 3)+(3\times 4)+(4\times 5)+(5\times 6)$

Observe the following pattern

$1=\frac{1}{2}\{1\times (1+1\left)\right\}$

$1+2=\frac{1}{2}\{2\times (2+1\left)\right\}$

$1+2+3=\frac{1}{2}\{3\times (3+1\left)\right\}$

$1+2+3+4=\frac{1}{2}\{4\times (4+1\left)\right\}$

and find the values of each of the following:

$1+2+3+4+5+......+50$

Observe the following pattern

$1=\frac{1}{2}\{1\times (1+1\left)\right\}$

$1+2=\frac{1}{2}\{2\times (2+1\left)\right\}$

$1+2+3=\frac{1}{2}\{3\times (3+1\left)\right\}$

$1+2+3+4=\frac{1}{2}\{4\times (4+1\left)\right\}$

and find the values of each of the following:

$31+32+......+50$

Observe the following pattern

$1^2=\frac{1}{6}[1\times (1+1)\times (2\times 1+1\left)\right]$

$1^2+2^2=\frac{1}{6}[2\times (2+1)\times (2\times 2+1\left)\right]$

$1^2+2^2+3^2=\frac{1}{6}[3\times (3+1)\times (2\times 3+1\left)\right]$

$1^2+2^2+3^2+4^2=\frac{1}{6}[4\times (4+1)\times (2\times 4+1\left)\right]$

and find the values of each of the following:

$1^2+2^2+3^2+4^2+.....+{10}^2$

Observe the following pattern

$1^2=\frac{1}{6}[1\times (1+1)\times (2\times 1+1\left)\right]$

$1^2+2^2=\frac{1}{6}[2\times (2+1)\times (2\times 2+1\left)\right]$

$1^2+2^2+3^2=\frac{1}{6}[3\times (3+1)\times (2\times 3+1\left)\right]$

$1^2+2^2+3^2+4^2=\frac{1}{6}[4\times (4+1)\times (2\times 4+1\left)\right]$

and find the values of each of the following:

$5^2+6^2+7^2+8^2+9^2+{10}^2+{11}^2+{12}^2$

Which of the following numbers are squares of even numbers?

$121, 225, 256, 324, 1296, 6561, 5476, 4489, 373758$