Question

A Geometric progression (GP) consists of 200 terms . if the sum of odd terms of the GP is m, and the sum of the even terms of the GP is n, then what is its common ratio?

Answer 1

Answer :

r = n/m

Solution :

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ar199

|–––|–––––––––––––––––––|

a ar⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 200

odd terms = a, ar², ar^4, ............ ar^198

even terms = ar, ar³ , ar^5,............. ar^199

sum = m

common ratio = r²

= a(1 - r²)^100/1 - r = m

= ar(1 - r²)^100/1 - r = n

dividing

= 1/r = m/n

= r = n/m