Question

Sum of all multiples of 6 between 200 and 1100

Answer 1

therefore sum of all multiples of 6 between 200 and 1100 is 97650

Answer 2

Answer:

Sum of all multiples of 6 between 200 and 1100 is 97650.

Step-by-step explanation:

To find : Sum of all multiples of 6 between 200 and 1100 ?

Solution :

Multiples of 6 between 200 and 1100 is 204,210,....,1098.

This form an arithmetic progression.

Where, first term is a=204 and common difference d=6

last term is l=1098

First we find number of terms,

$l=a+(n-1)d$

$1098=204+(n-1)6$

$1098-204=(n-1)6$

$894=(n-1)6$

$n-1=\frac{894}{6}$

$n-1=149$

$n=150$

Now, The sum of A.P formula is

$S_n=\frac{n}{2}[2a+(n-1)d]$

$S_{150}=\frac{150}{2}[2(204)+(150-1)6]$

$S_{150}=\frac{150}{2}[408+6\times 149]$

$S_{150}=75[408+894]$

$S_{150}=75[1302]$

$S_{150}=97650$