How do you find the explicit formula for the following sequence 1/3,2/9,4/27,8/81,16/243......?

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How do you find the explicit formula for the following sequence 1/3,2/9,4/27,8/81,16/243......?

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Answer 1 · 2016-02-15T01:43:29

$a_{n} = \frac{1}{3} \cdot {(\frac{2}{3})}^{n}$ $a_n=1/3*(2/3)^n$

Explanation:

$a_{0} = \frac{1}{3}$ $a_0=1/3$
$a_{1} = a_{0} \cdot \frac{2}{3} = \frac{2}{9}$ $a_1=a_0*2/3=2/9$
$a_{2} = a_{1} \cdot \frac{2}{3} = a_{0} \cdot {(\frac{2}{3})}^{2} = \frac{4}{27}$ $a_2=a_1*2/3 = a_0*(2/3)^2 =4/27$
$a_{3} = a_{2} \cdot \frac{2}{3} = a_{0} \cdot {(\frac{2}{3})}^{3} = \frac{8}{81}$ $a_3=a_2*2/3=a_0*(2/3)^3=8/81$
$a_{4} = a_{3} \cdot \frac{2}{3} = a_{0} \cdot {(\frac{2}{3})}^{4} = \frac{16}{243}$ $a_4=a_3*2/3=a_0*(2/3)^4=16/243$

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$a_{n} = a_{0} \cdot {(\frac{2}{3})}^{n} = \frac{1}{3} \cdot {(\frac{2}{3})}^{n}$ $a_n=a_0*(2/3)^n = 1/3*(2/3)^n$

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How do you find the explicit formula for the following sequence 1/3,2/9,4/27,8/81,16/243......?

1 Answer

Explanation:

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