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.

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Understanding CBSE Mathematics

Class :- 10th

Question no 53

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 – 56 = 7 and nth term(a

_{n}) = 497.By using the formula of nth term of an A.P.a_{n}= a + (n – 1)dSo,=> 497 = 56 + (n – 1)7

=> 7(n – 1) = 441

=> n – 1 = 63

=> n = 64

Now by using the formula of sum of n terms of an A.P.S_{n}= n[a + a_{n}] / 2So,S

_{64}= 64[56 + 497] / 2= 64[553]

= 17696

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