Question

Find the sum of integers between 100 and 200that are
(a) divisible by 9
(b) not divisible by 9

Answer 1

Step-by-step explanation:

(i) Number between 100−200 divisible by 9 are 108,117,126,...198

Here, a=108.d=117−108=9 and an=198

=a+(n−1)d=198

→ 108+(n−1)9=198

→ 9[12+n−1]=198⇒ n=22−11⇒ n=11

Now, Sn=2n[2a+(n−1)d]

⇒ S11=211[2(108)+(11−1)(9)]

=211[216+90]

=211×306

=11×153

⇒ S11=1683

(ii) Numbers between 100 and 200=101,102,103,....199

Here, a=101,d=1