This is the basic and conceptual question from Chapter name- Arithmetic Progression
Chapter number- 9
Exercise 9.6
In this question we have been asked to find the sum of the first 40 positive integers
CBSE DHANPAT RAI publications
Class:- 10th
Solutions of CBSE Mathematics
Question 11(ii)
We know sum of n terms of an A.P. is given by, Sn = n[2a + (n − 1)d] / 2.
(a) First 40 positive integers divisible by 3 are 3, 6, 9, 12,…… ,120.
These integers form an A.P. with first term(a) = 3,
Common difference(d) = 6 − 3 = 3 and number of terms(n) = 40.
S40 = 40[2(3) + (40 − 1)3]/2
= 40(6 + 117)/2
= 20(123) = 2460
Hence, the sum of first 40 multiples of 3 is 2460.
(b) First 40 positive integers divisible by 5 are 5, 10, 15, 20,…… ,200.
These integers form an A.P. with first term(a) = 5,
Common difference(d) = 10 − 5 = 5 and number of terms(n) = 40.
S40 = 40[2(5) + (40 − 1)5]/2
= 40(10 + 195)/2
= 20(205) = 4100
Hence, the sum of first 40 multiples of 5 is 4100.
(c) First 40 positive integers divisible by 6 are 6, 12, 18, 24,…… ,240.
These integers form an A.P. with first term(a) = 6,
Common difference(d) = 12 − 6 = 6 and number of terms(n) = 40.
S40 = 40[2(6) + (40 − 1)6]/2
= 40(12 + 234)/2
= 20(246) = 4920
Hence, the sum of first 40 multiples of 6 is 4920.