Question

4.6 arithmetic sequences for use with exploration 4.6
essential question how can you use an arithmetic sequence to describe a pattern?
an arithmetic sequence is an ordered list of numbers in which the difference between each pair of consecutive terms, or numbers in the list, is the same.
1 exploration: describing a pattern
go to bigideasmath.com for an interactive tool to investigate this exploration.
work with a partner. use the figures to complete the table. plot the points given by your completed table. describe the pattern of the y - values.
a. n = 1 n = 2 n = 3 n = 4 n = 5
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number of stars, n	1	2	3	4	5
number of sides, y

b. n = 1 n = 2 n = 3 n = 4 n = 5
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n	1	2	3	4	5
number of circles, y

Explanation:

Step1: Analyze part a

A single star has 5 sides. When \(n = 1\), \(y=5\); when \(n = 2\), there are 2 stars and \(y = 5\times2=10\); when \(n = 3\), \(y=5\times3 = 15\); when \(n = 4\), \(y=5\times4=20\); when \(n = 5\), \(y=5\times5 = 25\).

Step2: Analyze part b

When \(n = 1\), there is 1 circle, so \(y = 1\); when \(n=2\), there are 2 circles, \(y = 2\); when \(n = 3\), there are 3 circles, \(y=3\); when \(n = 4\), there are 4 circles, \(y = 4\); when \(n=5\), there are 5 circles, \(y = 5\).

Step3: Describe the patterns

In part a, the \(y - values\) form an arithmetic - sequence with a common difference of 5 and a first - term of 5. In part b, the \(y - values\) form an arithmetic sequence with a common difference of 1 and a first - term of 1.

Answer:

a.

Number of stars, \(n\)	1	2	3	4	5

b.

\(n\)	1	2	3	4	5