Section 12.1 Sequences and Section 12.2 Arithmetic Sequences

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

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

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

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

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

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

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

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

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

Copyright © 2013 Pearson Education, Inc. All rights reserved

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

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

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

Find the sum: 52 + 57 + 62 + 67 + … + 122 Copyright © 2013 Pearson Education, Inc. All rights reserved

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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