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Question

# Identify a pattern in each list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.) $1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}$, ____

Solution

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Answered 2 years ago
Answered 2 years ago
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Each number is found by adding 1 to the denominator of the previous number. Note that the denominator of 1 is 1:

\begin{align*} \dfrac{1}{1+1}&=\dfrac{1}{2}\\ \dfrac{1}{2+1}&=\dfrac{1}{3}\\ \dfrac{1}{3+1}&=\dfrac{1}{4}\\ \dfrac{1}{4+1}&=\dfrac{1}{5} \end{align*}

So, the next number is:

$\dfrac{1}{5+1}=\color{#c34632}\dfrac{1}{6}\color{white}\tag{1}$

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