Question

A geometric sequence is defined by the general term t^n = 75(5^n), where n ∈N and n ≥ 1. What is the recursive formula of the sequence?

A) t^1 = 75, t^n = 5t^n - 1, where n ∈N and n > 1
B) t^1 = 75, t^n = 75t^n - 1, where n ∈N and n > 1
C) t^1 = 375, t^n = 5t^n - 1, where n ∈N and n > 1
D) t^1 = 375, t^n = 5t^n + 1, where n ∈N and n > 1

Please help! I'm really confused.

Answer 1

note that 5^n multiples by 5 for each increase in n.
So, B is out.
when n=1, 75*5^1 = 375, so that is t^1
C is correct, if written 5^(n-1)

rather than t^n you should write tn or t_n to avoid confusing the subscript with an exponent.

Answer 2

oops. I meant t_(n-1), not t^(n-1)
see what I meant?

Answer 3

thank you steve