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)
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.