How do you write the formula for the nth term given 900, 300, 100, 33 1/3,...?

1 Answer
Apr 2, 2016

900*(1/3)^(n-1)

Explanation:

Each term after the first is equal to the previous term multiplied by 1/3. If we do not simplify at each step, and simply group the 1/3s together, then we can rewrite the sequence as

900, 900*1/3, 900*(1/3)^2, 900*(1/3)^3, ...

and from this it is evident that the n^"th" term may be written as 900*(1/3)^(n-1).

This type of sequence is called a geometric sequence. A geometric sequence is a sequence of the form a_0, a_0r, a_0r^2, ... where a_0 is the starting term and r is the common ratio between terms. In this case, we'd have a_0 = 900 and r = 1/3.