Question

Verify whether the following sequence is G.P. If so, write t_n:

2, 6, 18, 54, ...

Answer 1

2, 6, 18, 54, ...
t₁ = 2, t₂ = 6, t₃ = 18, t₄ = 54, …

Here,  `"t"_2/"t"_1 = "t"_3/"t"_2 = "t"_4/"t"_3` = 3

Since, the ratio of any two consecutive terms is a constant, the given sequence is a geometric progression.
Here. a = 2, r = 3
t_n= ar^n–1
∴ t_n = 2(3^n–1)