Question

Find the sum of all multiples of 7 lying between 500 and 900.

Answer 1

The multiples of 7 lying between 500 and 900 are 504, 511, 518, … , 896.

This is an A.P.

First term, a = 504

Common difference, d = 511 − 504 = 7

Last term = 896

Let there be n terms in the A.P.

`a_n=896`

`rArr a+(n+1)d=896`

`rArr 504+(n-1)xx7=896`

`rArr (n-1)xx7=896-504`

`rArr (n-1)=392/7`

`rArr n-1=56`

`rArr n=57`

We know that, `S_n=n/2(a+l)`

∴Sum of all the multiples of 7 lying between 500 and 900

`=57/2(504+896)`

`=57/2xx1400`

`=57xx700`

`=39900`

Thus, the sum of all the multiples of 7 lying between 500 and 900 is 39900.