If the first,second and fifth terms of AP are three consecutive terms of a GP,find the common ratio?

Answer 1

for the AP
first term = a
2nd term = a+d
fifth term = a+4d

but these also form a GP, so
(a+d)/a = (a+4d)/(a+d)
a^2 + 2ad + d^2 = a^2 + 5ad
3ad = d^2
d = 3a

common ratio
= (a+d)/a
= (a+3a)/a = 4

Answer 2

the answer is 3

Answer 3

answer is 3