The second and fifth terms of a geometric progression (GP) are 1 and 1 respectively.find (a) common ratio

Question

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8

Answer 1

Use your definitions

2nd term : ar = 1
5th term : ar^4 = 1

divide:
r^3 = 1
r = 1

the ar = 1
a(1) = 1
a = 1

your GP is 1,1,1,....
(not a very exciting sequence, some authors would exclude r = 1 in a GP)

Answer 2

I think that the attempt at including a fraction has bungled the posting. I read it as

The second and fifth terms of a geometric progression (GP) are 1 and 1/8 respectively. Find (a) common ratio

T5/T2 = r^3 = 1/8
so,
r = 1/2