Try the fastest way to create flashcards
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

Verified
Answered 2 years ago
Answered 2 years ago
Step 1
1 of 2

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:

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

## Recommended textbook solutions

#### Thinking Mathematically

7th EditionISBN: 9780134683713 (2 more)Robert F. Blitzer
9,671 solutions

#### Probability and Statistics for Engineers and Scientists

9th EditionISBN: 9780321629111 (4 more)Keying E. Ye, Raymond H. Myers, Ronald E. Walpole, Sharon L. Myers
1,204 solutions

#### The Practice of Statistics for the AP Exam

5th EditionISBN: 9781464108730 (1 more)Daniel S. Yates, Daren S. Starnes, David Moore, Josh Tabor
2,433 solutions

#### Statistics and Probability with Applications

3rd EditionISBN: 9781464122163Daren S. Starnes, Josh Tabor
2,555 solutions
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 29, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}