If a+b+...+l is a GP, prove that its sum is bl-a^2/b-a

given: a,b, ........I are in GP.
therefore 
common ratio r = b/a
let the number of terms in GP be n.
therefore the sum of n terms of GP is a(rn-1)r-1 [since a is the first term of GP]
nth term of GP is I=a.rn-1rn-1=Ia
therefore rn=r.rn-1=r.Iarn=ba.Ia=bIa2
sum =abIa2-1ba-1=a.bI-a2a2b-aa
=bI-a2b-a

hope this helps you

  • 15
What are you looking for?