Question

Prove that the (n+1) term of a G.P of which the first term is a and third term is b,is equal to the (2n+1) term of a G.P of which the first term is a and fifth term is b.

Answer 1

Hello,


`u_(1) =a\\ u_(3) =b\\ q= (\frac { u_(3) } {u_(1 ) } )^ (1)/(2) \\\\\\ =((b)/(a)) ^ (1)/(2) \\ u_(n+1) =a*q^(n)=a* ((b)/(a)) ^ (n)/(2) \\ \\\\\\\\\\\\v_(1) =a\\ v_(5) =b\\ r= (\frac { v_(5) } {v_(1 ) } )^ (1)/(4) \\\\\\ v_(2n+1) =a*r^(2n)\\\\ =a* ((b)/(a)) ^ (2n)/(4)\\\\ =a* ((b)/(a)) ^ (n)/(2) \\`