Question

A geometric sequence is defined by a the recursive formula t1 = 243, tn + 1 = tn/3

where n ∈N and n ≥ 1. The general term of the sequence is

Answer 1

tn = 243·(1/3)^(n-1)

Explanation:

The recursive formula tells you the first term (243) and the common ratio (1/3). You can put these numbers into the general formula for the n-th term of a geometric sequence:

an = a1·r^(n-1) . . . . . where a1 is the first term and r is the common ratio

You want the n-th term of your sequence to be called tn, so ...

tn = 243·(1/3)^(n-1)