Question

Find the sum of all numbers between 100 and 200 which are not divisible by 9

Answer 1

Sum = 13167

Step-by-step explanation:

The sum integers between 100 and 200 that are not divisible by 9.

First we find how many numbers between 100 and 200 divisible by 9

First term (a) = 108

Common Difference (d) = 9

Last term (l)=198

Formula: a_n=a+(n-1)da

n

=a+(n−1)d

198=108+(n-1)9

n=11

Now we find sum of these 11 terms

Formula: S_n=\frac{n}{2}(2a+(n-1)d)S

n

=

2

n

(2a+(n−1)d)

S_{11}=\frac{11}{2}(108(2)+10(9))S

11

=

2

11

(108(2)+10(9))

Sum of 11 term = 1683

Now we find the sum of series 101,102,103,.........,199

S_{99}=\frac{99}{2}(101(2)+98(1))S

99

=

2

99

(101(2)+98(1))

Sum of 99 terms = 14850

Sum of integers between 100 and 200 not divisible by 9 = 14850 - 1683 = 13167

Hence, The sum of number not divisible by 9 between 100 and 200 is 13167

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