# Find the sum of the integers between 100 and 200 that are divisible by 9 - Mathematics

Sum

Find the sum of the integers between 100 and 200 that are divisible by 9

#### Solution

The numbers (integers) between 100 and 200 which is divisible by 9 are 108, 117,126, ..., 198

Let n be the number of terms between 100 and 200 which is divisible by 9.

Here, a = 108, d = 117 – 108 = 9

And an = l = 198

\implies 198 = 108 + (n – 1)9   ......[∵ an = l = a + (n – 1)d]

\implies 90 = (n – 1)9

\implies n – 1 = 10

\implies n = 11

∴ Sum of terms between 100 and 200 which is divisible by 9 is

Sn = n/2 [2a + (n - 1)d]

\implies S11 = 11/2[2(108) + (11 - 1)9]

= 11/2[216 + 90]

= 11/2 xx 306

= 11 × 153

= 1683

Hence, required sum of the integers between 100 and 200 that are divisible by 9 is 1683.

Concept: Sum of First n Terms of an A.P.
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Chapter 5: Arithematic Progressions - Exercise 5.4 [Page 57]

#### APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 5 Arithematic Progressions
Exercise 5.4 | Q 5.(i) | Page 57

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