Question

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

1, – 5, 25, – 125, ...

Answer 1

1, – 5, 25, – 125, ...
t₁ = 1, t₂ = – 5, t₃ = 25, t₄ = –125, …

Here, `"t"_2/"t"_1  = "t"_3/"t"_2 = "t"_4/"t"_3` = – 5

Since, the ratio of any two consecutive terms is a constant, the given sequence is a geometric progression.
Here, a = 1, r = – 5
t_n = ar^n–1
∴  t_n = (– 5)^n–1