Find the sum of the integers between 100 and 200 that are not divisible by 9
Solution:
Given, the series is the integers between 100 and 200 that are not divisible by 9.
We have to find the sum of the series.
The integers between 100 and 200 are 101, 102, 103,......,199.
Here, first term, a = 101
Last term, l = 199
Common difference, d = 1
The nth term of the series in AP is given by
aₙ = a + (n - 1)d
199 = 101 + (n - 1)1
199 - 101 = n - 1
98 + 1 = n
n = 99
If l is the last term of an AP, then the sum of the terms is given by
S = n/2[a+l]
So, S = 99/2[101 + 199]
= 99/2[300]
= 99(150)
S = 14850
The integers between 100 and 200 that are divisible by 9 are 108, 117, 126,.......,198
Therefore, the series is 108, 117, 126,......., 198.
First term, a = 108
Last term, l = 198
Common difference, d = 9
The nth term of the series in AP is given by
aₙ = a + (n - 1)d
So, 198 = 108 + (n - 1)9
198 - 108 = 9n - 9
90 + 9 = 9n
9n = 99
n = 99/9
n = 11
If l is the last term of an AP, then the sum of the terms is given by
S = n/2[a+l]
So, S = 11/2[108+198]
= 11/2[306]
= 11(153)
S = 1683
Sum of the integers between 100 and 200 that are not divisible by 9 = (Sum of the integers between 100 and 200) - (sum of the integers between 100 and 200 that are divisible by 9)
= 14850 - 1683
= 13167
Therefore, the sum of the integers between 100 and 200 that are not divisible by 9 is 13167.
✦ Try This: Find the sum of integers between 300 and 500 that are not divisible by 14
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5
NCERT Exemplar Class 10 Maths Exercise 5.4 Problem 5 (ii)
Find the sum of the integers between 100 and 200 that are not divisible by 9
Summary:
The sum of the integers between 100 and 200 that are not divisible by 9 is 13167
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