Question: "Write the formula for the nth term given..."

djo57bgfrqn

Answered question

2022-10-13

Write the formula for the nth term given 900, 300, 100, 33 1/3,...

Davin Meyer

Beginner2022-10-14Added 13 answers

Each term after the first is equal to the previous term multiplied by

\frac{1}{3}

. If we do not simplify at each step, and simply group the

\frac{1}{3}

s together, then we can rewrite the sequence as

900, 900 \cdot \frac{1}{3}, 900 \cdot {(\frac{1}{3})}^{2}, 900 \cdot {(\frac{1}{3})}^{3}, ...

and from this it is evident that the

n^{th}

term may be written as

900 \cdot {(\frac{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_{0} r, a_{0} r^{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 = \frac{1}{3}

900 \cdot {(\frac{1}{3})}^{n - 1}

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