Question

The first, third and fifth term of the geometric sequences forms the first three consecutive terms of A.P.If the first term of the sequences is 2,find the sum of the first ten terms

Answer 1

You are saying that:
a , ar^2, and ar^4 form an AS
and since a = 2
we have:
2, 2r^2 and 2r^4 form an AS
that is:
2r^2 - 2 = 2r^4 - 2r^2
r^2 - 1 = r^4 - r^2
r^2 - 1 = r^2(r^2 - 1)
divide by r^2 - 1, r ≠ ±1
1 = r^2
so r = ± 1

dilemna!!! , we said r ≠ ±1
only way this is possible if the GS is
2, 2, 2, 2, 2, 2, .... , not a very exciting sequence
or
2, -2, 2 , -2, 2, .... and the first , third and 5th indeed do form an AS

Am I misreading the question??