Question

25 से 180 तक की सम संख्याओं का औसत क्या
होगा?​

Answer 1

$\huge{\mathbb{\red{ANSWER:-}}}$

$25 --------> 180$

$26 , 28 , 30 , 32 ,..........., 180$

$a = 26$

$d = 2$

$An = 180$

$\small\boxed{An=a+(n-1)d}$

$where-$

$a= first \: term$

$d = common \: difference$

$\: \: \: \: An = last \: term$

$\: \: \: 180 = 26 + (n-1)2$

$\: \: \: 154 = 2(n - 1)$

$\: \: (n - 1) = 77$

$\: \: \: \: n = 78$

$Sum \: of \: all \: even \: numbers \: from$

$25 \: to \: 180.$

$\small\boxed{Sn=\dfrac{n}{2}[a + An]}$

$\: \: \: \: \: n = Total \: terms = 78$

$S(78) =\frac{78}{2}[26 + 180]$

$\: \: \: = 39 * 206$

$\: \: \: = 39 * (200 + 6)$

$\: \: \: = 7800 + 234$

$\: \: \: = 8034$

$Now ,$

$\small\boxed{average=\dfrac{Sum \: of \: all \: terms}{Total \: terms}}$

$Average \: of \: all \: 78 \: even \: no.-$

$=\frac{8034}{78}$

$=\frac{39 * 206}{78}$

$=\frac{206}{2}$

$= 103$

$Short \: explanation:-$

$In \: the \: case \: of \: consecutive \: terms-$

$Average=\dfrac{1st \: term + last \: term}{2}$

$\: \: \: \: \: \: =\frac{26+180}{2}$

$\: \: \: \: \: \: =\frac{206}{2}$

$\: \: \: \: \: \: = 103$