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# Question 12. Find the sum of (iv) all 3–digit natural numbers which are multiples of 11.

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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)

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### 1 Answer

1. 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.

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