Find the sum of all even numbers between 2 & 200 inclusive, excluding those which are multiples of 3.
Sum of even numbers, is it means the series of
2 + 4 + 6 + ….+ 200?
Excluding multiples of 3, is it means
6 + 12 + 18 +....+ 198?
{ $\displaystyle x$ :2≤ $\displaystyle x$ ≤200 }
$\displaystyle 4,6,8,...,198 \quad A.P.$
$\displaystyle a=4$
$\displaystyle d=2$
$\displaystyle n=98$
$\displaystyle S_A=0.5n(a+l)$
$\displaystyle S_A=0.5(98)[(4)+(198)]$
$\displaystyle 6,12,18,...,198 \quad A.P.$
$\displaystyle a=6$
$\displaystyle d=6$
$\displaystyle n=33$
$\displaystyle S_B=0.5n(a+l)$
$\displaystyle S_B=0.5(33)[(6)+(198)]$
$\displaystyle S_A-S_B$