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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. All 2-digit natural numbers divisible by 4 are 12, 16, 20,â€¦â€¦ ,96.

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

and common difference(d) = 16 âˆ’ 12 = 4.

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

=> 96 = 12 + (n âˆ’ 1)4

=> 4(n âˆ’ 1) = 84

=> Â n âˆ’ 1 = 21

=> n = 22

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

S22Â = 22[2(12) + (22 âˆ’ 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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