Question

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

Answer 1

Answer:

17822

Step-by-step 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 :

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

Putting all the values,

$S_n=\dfrac{67}{2}[2(35)+(67-1)7]\\\\S_n=17822$

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