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 100 and 550 which are divisible by 9.
CBSE DHANPAT RAI PUBLICATIONS
Understanding CBSE Mathematics
Class :- 10th
Question no 55(i)
All integers between 100 and 550 which are divisible by 9 are 108, 117, 126, 135, . . . .549.
First term(a) = 108, common difference(d) = 117 – 108 = 9 and nth term(an) = 549.
By using the formula of nth term of an A.P.
an = a + (n – 1)d
So,
=> 549 = 108 + (n – 1)9
=> 9(n – 1) = 441
=> n – 1 = 49
=> n = 50
Now by using the formula of sum of n terms of an A.P.
Sn = n[a + an] / 2
So,
S50 = 50[108 + 549]/2
= 25[657]
= 16425
Hence, sum of all integers between 100 and 550 which are divisible by 9 is 16425.