What is the value of n if the sum of n terms of the G.P. 2,23,29 ...is8027?
Answer:
4
- In the given G.P., the first term, a=2 and
the common ratio, r=ak+1ak where k≥1
⟹r=232=13 - The sum of first n terms of this G.P. is given by,
Sn=a(1−rn)(1−r)=8027⟹2(1−(13)n)1−13=8027⟹2(1−(13)n)23=8027⟹62[1−(13)n]=8027⟹[1−(13)n]=8081⟹(13)n=1−8081⟹13n=181⟹3n=34⟹n=4