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Question 12. Find the sum of (v) all 2-digit natural numbers divisible by 4.

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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 to find the sum of all 2-digit natural numbers divisible by 4.

CBSE DHANPAT RAI publication
CBSE Mathematics Class 10th
Question 12(v)

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1 Answer

  1. All 2-digit natural numbers divisible by 4 are 12, 16, 20,…… ,96.

    These numbers form an A.P. with first term(a) = 4

    and common difference(d) = 16 − 12 = 4.

    We know, the nth term of an A.P. is given by, an = a + (n − 1)d.

    => 96 = 12 + (n − 1)4

    => 4(n − 1) = 84

    =>  n − 1 = 21

    => n = 22

    Also, we know sum of n terms of an A.P. is given by, Sn = n[2a + (n − 1)d] / 2.

    S22 = 22[2(12) + (22 − 1)4]/2

    = 22[24 + 84]/2

    = 22[54] = 1188

    Hence, the sum of all 2-digit natural numbers divisible by 4 is 1188.

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