Question

Find the sum of the numbers divisible by 7 between 30 and 500

Answer 1

17822

Explanation:

The number that are divisible by 7 between 30 and 500 are as follows :

35, 42,49,.....,497

It will form an AP with first term, a = 35 and common difference, d = 7

Let there are n terms in the AP.

nth term of an AP is given by :

`a_n=a+(n-1)d`

Putting all the values,

`497=35+(n-1)7\\\\462=(n-1)7\\\\n-1=66\\\\n=67`

Now, the sum of n terms of an AP is given by :

`S_n=(n)/(2)[2a+(n-1)d]`

Putting all the values,

`S_n=(67)/(2)[2(35)+(67-1)7]\\\\S_n=17822`

Hence, the sum of the numbers that are divisible by 7 between 30 and 500 is 17822.