Suppose you are given t_2=18 and t_4=8. How can you find two different possible ratios?

Question

how can you also find the two sequences having these terms?

Answer 1

I dont know what you mean by the two different ratios, maybe t_2 / t_4 (18/8 = 9/4), and t_4 / t_2 (8/18 = 4/9). But two sequences that have these in it could be: ( i found by doing the following)
t_4 = t_2 - 2x
8 = 18 - 2x
x = 5

This could be one, it is recursive:
t_n = t_(n-1) - 5
Heres another, not recursive, i just added 5 to t_2, to get t_1 (23), then made it from that:
t_n = 23 - 5 * (n-1)

I hope that helps.

Answer 2

supposing that we are dealing with a geometric sequence
t_4=t_2*r^2 so
r^2=8/18 and r =+- 2/3
Taking r=2/3
t_1=27 t_2=18 t_3=12 and t_4 =8
if we take r= -2/3
t_1=-27 t_2=18 and so on