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Section 12.1 Sequences and Section 12.2 Arithmetic Sequences

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1 Section 12.1 Sequences and Section 12.2 Arithmetic Sequences
Copyright © 2013 Pearson Education, Inc. All rights reserved

2 Write the first several terms of a sequence.
Objectives Write the first several terms of a sequence. Write the terms of a sequence defined by a recursive formula. Use summation notation. Find the sum of a sequence algebraically. Determine if a sequence is arithmetic. Find a formula for an arithmetic sequence. Find the sum of an arithmetic sequence. Copyright © 2013 Pearson Education, Inc. All rights reserved

3 Copyright © 2013 Pearson Education, Inc. All rights reserved

4 Copyright © 2013 Pearson Education, Inc. All rights reserved

5 Copyright © 2013 Pearson Education, Inc. All rights reserved

6 Copyright © 2013 Pearson Education, Inc. All rights reserved

7 Copyright © 2013 Pearson Education, Inc. All rights reserved

8 Copyright © 2013 Pearson Education, Inc. All rights reserved

9 Sometimes a sequence is defined by assigning a value to the first term and specifying the nth term by a formula that uses preceding term(s). This is called a recursive formula. Copyright © 2013 Pearson Education, Inc. All rights reserved

10 Write down the first five terms of the following recursively defined sequence.
Copyright © 2013 Pearson Education, Inc. All rights reserved

11 Write down the first five terms of the following recursively defined sequence.
Copyright © 2013 Pearson Education, Inc. All rights reserved

12 Copyright © 2013 Pearson Education, Inc. All rights reserved

13 Copyright © 2013 Pearson Education, Inc. All rights reserved

14 Copyright © 2013 Pearson Education, Inc. All rights reserved

15 Copyright © 2013 Pearson Education, Inc. All rights reserved

16 Copyright © 2013 Pearson Education, Inc. All rights reserved

17 Copyright © 2013 Pearson Education, Inc. All rights reserved

18 Arithmetic Sequence Copyright © 2013 Pearson Education, Inc. All rights reserved

19 Show that the sequence is arithmetic
Show that the sequence is arithmetic. List the first term and the common difference. (a) 4, 2, 0, -2, . . . Copyright © 2013 Pearson Education, Inc. All rights reserved

20 Copyright © 2013 Pearson Education, Inc. All rights reserved

21 Find the twenty fourth term of the arithmetic sequence:
–3, 0, 3, 6, . . . Copyright © 2013 Pearson Education, Inc. All rights reserved

22 Copyright © 2013 Pearson Education, Inc. All rights reserved

23 Copyright © 2013 Pearson Education, Inc. All rights reserved

24 Find the sum of the first n terms of the sequence {4n + 2}
Copyright © 2013 Pearson Education, Inc. All rights reserved

25 Find the sum: … + 122 Copyright © 2013 Pearson Education, Inc. All rights reserved

26 Homework 12.1 # 13, 19, 21, 29, 35, 37, 45, 53, 63, 65, 75, 77 12.2 # 7, 11, 17, 19, 23, 27, 29, 37,41, 49 Copyright © 2013 Pearson Education, Inc. All rights reserved


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