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Question

Question 5 (ii)
Find the sum of the integers between 100 and 200 that are not divisible by 9.

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Solution

The sum of the integers between 100 and 200 which is not divisible by 9 = ( sum of total numbers between 100 and 200) – (sum of total numbers between 100 and 200 which is divisible by 9).
Here, a = 101, d =102 – 101 = 1 and an = l = 199
an=l=a+(n1)d
199=101+(n1)1
(n1)=98n=99
Sum of terms between 100 and 200,
Sn=n2[2a+(n1)d]
S99=992[2(101)+(991)1]=992[202+98]
=992×300=99×150=14850
Therefore, sum of the integers between 100 and 200 which is not divisible by 9,
= 14850 – 1683
= 13167
Hence, the required sum is 13167.

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