Question

Find the sum of all numbers from 1 to 200 which are divisible by 6

Answer 1

$\bold\red{\underline{\underline{Answer:}}}$

$\bold{Sum \ of \ all \ numbers \ from \ 1 \ to \ 200}$

$\bold{which \ are \ divisible \ by \ 6 \ is \ 3366.}$

$\bold\purple{Explanation}$

To get sum of number divided by 6 from 1 to 200, we must form an A.P. of multiples of 6 from 1 to 200 and then sum of that A.P.

$\bold\green{\underline{\underline{Solution}}}$

A.P. will be:-

6,12,18,...,198

Here,t1=6,d=12-6=6,tn=198

tn=a+(n-1)d...formula

198=6+(n-1)6

(n-1)6=198-6

(n-1)6=192

$\bold{n-1=\frac{192}{6}}$

n-1=32

n=32+1

n=33

$\bold{Sn=\frac{n}{2}[t1+tn]... formula}$

$\bold{S33=\frac{33}{2}[6+198]}$

$\bold{S33=\frac{33}{2}×204}$

$\bold{S33=33×102}$

$\bold{S33=3366}$

Therefore,

$\bold\purple{Sum \ of \ all \ numbers \ from \ 1 \ to \ 200}$

$\bold\purple{which \ are \ divisible \ by \ 6 \ is \ 3366.}$