9­3 Arithmetic Sequences and Series­ period 1.notebook
April 23, 2015
Bellwork 4-23-15
Write a possible explicit rule for the nth term of each sequence.
1. 4, 5, 6, 7, 8,…
2. –3, –1, 1, 3, 5, …
3.
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9­3 Arithmetic Sequences and Series­ period 1.notebook
April 23, 2015
Because arithmetic sequences have a common difference, you
can use any two terms to find the difference.
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9­3 Arithmetic Sequences and Series­ period 1.notebook
April 23, 2015
Example 3: Finding Missing Terms
Find the missing terms in the arithmetic sequence
17,
,
,
, –7.
Step 1 Find the common difference.
Step 2 Find the missing terms.
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9­3 Arithmetic Sequences and Series­ period 1.notebook
April 23, 2015
Check It Out! Example 3
Find the missing terms in the arithmetic sequence
2, , , , 0.
Step 1 Find the common difference.
Step 2 Find the missing terms.
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9­3 Arithmetic Sequences and Series­ period 1.notebook
April 23, 2015
Example 4: Finding the nth Term Given Two Terms
Find the 5th term of the arithmetic sequence with a8 = 85 and
a14 = 157.
Step 1 Find the common difference.
Step 2 Find a1.
Step 3 Write a rule for the sequence, and evaluate to find a5.
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9­3 Arithmetic Sequences and Series­ period 1.notebook
April 23, 2015
Check It Out! Example 4a
Find the 11th term of the arithmetic sequence.
a2 = –133 and a3 = –121
Step 1 Find the common difference.
Step 2 Find a1.
Step 3 Write a rule for the sequence, and evaluate to find a11.
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9­3 Arithmetic Sequences and Series­ period 1.notebook
April 23, 2015
Check It Out! Example 4b
Find the 11th term of each arithmetic sequence.
a3 = 20.5 and a8 = 13
Step 1 Find the common difference.
Step 2 Find a1.
Step 3 Write a rule for the sequence, and evaluate to find a11.
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9­3 Arithmetic Sequences and Series­ period 1.notebook
April 23, 2015
An arithmetic series is the indicated sum of the terms of an
arithmetic sequence. You can derive a general formula for the
sum of an arithmetic series by writing the series in forward and
reverse order and adding the results.
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9­3 Arithmetic Sequences and Series­ period 1.notebook
April 23, 2015
Example 5A: Finding the Sum of an Arithmetic Series
Find the indicated sum for the arithmetic series.
S18 for 13 + 2 + (–9) + (–20) + ...
Find the common difference.
Find the 18th term.
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9­3 Arithmetic Sequences and Series­ period 1.notebook
April 23, 2015
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9­3 Arithmetic Sequences and Series­ period 1.notebook
April 23, 2015
Example 5B: Finding the Sum of an Arithmetic Series
Find the indicated sum for the arithmetic series.
Find 1st and 15th terms.
Find S15.
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9­3 Arithmetic Sequences and Series­ period 1.notebook
April 23, 2015
Check It Out! Example 5a
Find the indicated sum for the arithmetic series.
S16 for 12 + 7 + 2 +(–3)+ …
Find the common difference.
Find the 16th term.
Find S16.
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9­3 Arithmetic Sequences and Series­ period 1.notebook
April 23, 2015
Check It Out! Example 5b
Find the indicated sum for the arithmetic series.
Find 1st and 15th terms.
Find S15.
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9­3 Arithmetic Sequences and Series­ period 1.notebook
April 23, 2015
Homework: Worksheet 9-3 Practice B, #'s 9-17
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