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
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(an) = 497.
By using the formula of nth term of an A.P.
an = a + (n – 1)d
So,
=> 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.
Sn = n[a + an] / 2
So,
S64 = 64[56 + 497] / 2
= 64[553]
= 17696
Hence, the sum of all integers between 50 and 500 which are divisible by 7 is 17696.