Question

find the sum of integers between 1 and 200 which are multiples of 3 and 7

Answer 1

20100is your answer
I hope this helpzzzzzz.......

Answer 2

Given:

Multiples of 3 and 7 lying between 1 and 200  are

21,42,63,....189

To find:

Sum of integers lying between 1 and 200 which are multiples of 3 and 7.

Solution:

Total number of terms=n=9

First term=a=21

d=$a_2-a_1=42-21=21$

$a_3-a_2=63-42=21$

It is an A.P because the difference between two consecutive terms is constant.

Common difference=d=21

Sum of n terms of an A.P is given by

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

Using the formula

$S_9=\frac{9}{2}(2(21)+(9-1)(21))$

$S_9=\frac{9}{2}(42+168)=\frac{9}{2}(210)=9\times 105$

$S_9=945$

Hence, the sum of integers lying between 1 and 200 which are multiples of 3 and 7=945