One of the most important and exam oriented question from Chapter name- Arithmetic Progression
Class 10th
Chapter number- 9
Exercise :- 9.6
This type of question has been asked in previous years exams.
In this question we have been asked to find the sum of all integers between 100 and 550 which are not divisible by 9 by using arithmetic series sum formula.
CBSE DHANPAT RAI publication
CBSE Mathematics Class 10th
Question 55(ii)
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
Now, we know,
Sum of integers between 100 and 550 which are not divisible by 9 = Sum of integers between 100 and 550 – Sum of integers between 100 and 550 which are divisible by 9
= [101+102+103+104+. . . . .+549] – S50
= [1+2+3+4+. . . . +549] – [1+2+3+4+. . . .+100] – 16425
= 549[550]/2 – 100[101]/2 – 16425
= 150975 – 5050 – 16425
= 129500