Question

find the sum of integers lying between 750 and 1000 that are multiple of 13.​

Answer 1

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

$\bold{Sum \ of \ integers \ lying \ between \ 750}$

$\bold{and \ 1000 \ which \ are \ multiple \ of \ 13}$

$\bold{is \ 16549.}$

$\bold\pink{To \ find:}$

$\bold{Sum \ of \ integers \ lying \ between \ 750}$

$\bold{and \ 1000 \ which \ are \ multiple \ of \ 13.}$

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

$\bold{Numbers \ which \ lie \ between \ 750}$

$\bold{and \ 1000 \ which \ are \ multiple \ of \ 13}$

$\bold{are:-}$

$\bold{754,767,780,...,988}$

$\bold{The \ sequence \ forms \ an \ A.P.}$

$\bold{Here,a=754, \ d=13, \ tn=988}$

$\bold{tn=a+(n-1)d... formula}$

$\bold{988=754+(n-1)×13}$

$\bold{13(n-1)=988-754}$

$\bold{13(n-1)=234}$

$\bold{n-1=\frac{234}{13}}$

$\bold{n-1=18}$

$\bold{n=18+1}$

$\bold{n=19}$

__________________________________

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

$\bold{S19=\frac{19}{2}[754+988]}$

$\bold{S19=\frac{19}{2}×1742}$

$\bold{S19=19×871}$

$\bold{S19=16549}$

$\bold\purple{\tt{\therefore{Sum \ of \ integers \ lying \ between \ 750}}}$

$\bold\purple{\tt{and \ 1000 \ which \ are \ multiple \ of \ 13}}$

$\bold\purple{\tt{is \ 16549.}}$