How many terms of the GP 89,818,836..... should be added to get the sum 3118?
5
Here, a=89,r=81889=12 and Sn=3118.
Since Sn=a(1−rn)1−r is the sum of n terms of a GP of first term a and common ratio r, we have
3118=89×(1−(12)n)1−(12)
⇒ 3136=89×(1−(12)n)
⇒3132=1−(12)n
⇒1−3132=(12)n
⇒132=(12)n
i.e., 125=12n
⇒n=5