This is the basic and conceptual question from Chapter name- Arithmetic Progression
Chapter number- 9
Exercise 9.6
In this question we have to find the sum Of all 3–digit natural numbers which are multiples of 11.
CBSE DHANPAT RAI publications
Class:- 10th
Solutions of CBSE Mathematics
Question 12(iv)
All 3–digit natural numbers which are divisible by 11 are 110, 121, 132,…… ,990.
These numbers form an A.P. with first term(a) = 110 and
Common difference(d) = 121 − 110 = 11.
We know, the nth term of an A.P. id given by, an = a + (n − 1)d.
=> 990 = 110 + (n − 1)11
=> 990 = 110 + 11n -11
=> 990 = 99 + 11n
=> 11n = 891
=> n = 81
Also, we know sum of n terms of an A.P. is given by, Sn = n[2a + (n − 1)d] / 2.
S81 = 81[2(110) + (81 − 1)11]/2
= 81[1100]/2
= 81(550) = 44550
Hence, the sum of all 3–digit natural numbers which are divisible by 13 is 44550.