Question

the third term of GP is a square of first and fifth term is 64 find GP​

Answer 1

let the first term of the GP be a

=> second term will be ax

=> T3 = ax²

ATQ

T3 = a²

=> a² = ax²

=> x² = a

T5 = ax⁴ = a³

ATQ

T5 = 64

=>a³ = 64

=> a = 4

=> ax⁴ = 64

=> x = 2

=> GP is

4,8,16,32,64 .....

Answer 2

according to given condition,

third term of GP is a square of first term

therefore, [ar² = (a)²] on solving we get, (a=r²) this is 1st eqn..

then,5th term = 64

[ar⁴ = 64 ] this is 2nd eqn..

now substitute the value of (a) in eqn.

r².r⁴=64

r6 = (2)6

therefore,

[r = 2]... i think this will help u.