Find the sum of the integers between 100 and 200 that are:
(i) divisible by 9
(ii) not divisible by 9
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(i) Ap- 108, 117, 124,.....,198
nth term - 198
a nth term = a +( n-1)d
198 = 108+ (n-1) 9
198 = 108+ 9n - 9
198 = 99 + 9n
198 = 9 (11 + n)
11 + n = 198/9
11 + n = 22
n = 22 - 11
n = 11.
S11 = 11/2(a + l)
= 11/2(108 + 198)
= 11/2*306
= 11 * 153
= 1683
nth term - 198
a nth term = a +( n-1)d
198 = 108+ (n-1) 9
198 = 108+ 9n - 9
198 = 99 + 9n
198 = 9 (11 + n)
11 + n = 198/9
11 + n = 22
n = 22 - 11
n = 11.
S11 = 11/2(a + l)
= 11/2(108 + 198)
= 11/2*306
= 11 * 153
= 1683
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