Download 1.6 Notes: Arithmetic Sequence

Notes: Arithmetic Sequences
1.6: I can identify arithmetic sequences and patterns in a set of data. (G.1.c)
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Arithmetic Sequence
 An arithmetic sequence is a numerical pattern that increases or decreases at a constant
rate called the common difference.
Ex. (3, 5, 7, 9, 11, …)
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Ex. (33, 29, 25, 21, 17,…)
Identifying Arithmetic Sequences
1. Determine whether -15, -13, -11, -9, … is an arithmetic sequence. Explain.
7 5 1 −5
, … is
8
2. Determine whether 8 , 8 , 8 ,
an arithmetic sequence. Explain.
3. Determine whether 2, 4, 8, 10, 12, … is an arithmetic sequence.
a. Cannot be determined
b. This is not an arithmetic sequence because the difference between the terms is not constant.
c. This is an arithmetic sequence because the difference between terms is constant.
2
4 5
4. Determine whether 3 , 1, 3 , 3 , 2, … is an arithmetic sequence.
a. Cannot be determined
b. This is not an arithmetic sequence because the difference between the terms is not constant.
c. This is an arithmetic sequence because the difference between terms is constant.
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Identifying Arithmetic Sequences—EXTRA PRACTICE
Identify whether the following are examples of arithmetic sequences. If so, state the common difference.
5. (-3, -1, 1, 3, 5, 7, 9…)
6. (15.5, 14, 12.5, 11, 9.5, 8, …)
7. (84, 80, 74, 66, 56, 44, …)
8. (-8, 6, -4, 2, 0, …)
9. (-50, -44, -38, -32, -26, …)
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Finding the Next Term
10. Find the next three terms of the arithmetic sequence -8, -11, -14, -17, …
11. Find the next three terms of the arithmetic sequence 58, 63, 68, 73, …
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Finding the nth Term of an Arithmetic Sequence
Where:
𝑎𝑛 = the term that you want to find
𝑎1 = first term in the list of ordered numbers
𝑛 = the term position (ex: for 5th term, n = 5 )
𝑑 = common difference
12. Given: (79, 75, 71, 67, 63, …)
Find: 𝑎32
13. Given: (-11, -19, -27, -35,…)
Find: 𝑎19
14. Given: (-3, 1, 5, 9,…)
Find: 𝑎24
15. Given: (3.5, 6, 8.5, 11, …)
Find 𝑎100
16. Find the 78th term of the sequence (-12, -5, 2, 9, …).
17. Find the 112th term of the sequence (1, -2, -5, -8, …).
18. Find the 23rd term of the sequence ( 16, 21, 26, 31, … )
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Finding the term number, or term position
19. Given: (79, 75, 71, 67, 63, …)
Find: What term number (term position) is -169?
20. Given: (-62, -60, -58, -56, …)
Find: What term number (term position) is 16?
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Real World Connection:
Money: The arithmetic sequence 2, 7, 12, 17, 22, … represents the total number of pencils Claire has in
her collection after she goes to her school store each week.
A. Find the total number of pencils she will have after 12 weeks.