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

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

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Answer 1 · 2016-04-02T01:35:38

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

Explanation:

Each term after the first is equal to the previous term multiplied by $\frac{1}{3}$ $1/3$ . If we do not simplify at each step, and simply group the $\frac{1}{3}$ $1/3$ s 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 $r = 1/3$ .

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

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