• 0
Guru

# Question 53. Find the sum of all integers between 50 and 500 which are divisible by 7.

• 0

This is an arithmetic progression based question from Chapter name- Arithmetic Progression
Chapter number- 9
Exercise – 9.6
In this question we have been asked to Find the sum of all integers between 50 and 500 which are divisible by 7 by using the arithmetic series properties.

CBSE DHANPAT RAI PUBLICATIONS
Understanding CBSE Mathematics
Class :- 10th
Question no 53

Share

1. All integers between 50 and 500 which are divisible by 7 are 56, 63, 70, 77, . . . . 497.

First term(a) = 56, common difference(d) = 63 â€“ 56 = 7 and nth term(an) = 497.

By using the formula of nth term of an A.P.

anÂ = a + (n â€“ 1)d

So,Â

=> 497 = 56 + (n â€“ 1)7

=> 7(n â€“ 1) = 441

=> n â€“ 1 = 63

=> n = 64

Now by using the formula of sum of n terms of an A.P.

SnÂ = n[a + an] / 2

So,Â

S64Â = 64[56 + 497] / 2

= 64[553]

= 17696

Hence, the sum of all integers between 50 and 500 which are divisible by 7 is 17696.

• 0