1. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Recognize arithmetic sequences, and find the indicated term of an arithmetic sequence. Find arithmetic means between two numbers. 11.2 Arithmetic Sequences

2. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Glossary Terms arithmetic means arithmetic sequence common difference 11.2 Arithmetic Sequences

3. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties nth Term of an Arithmetic Sequence t n = t 1 + (n – 1)d 11.2 Arithmetic Sequences t n : nth term t 1 : first term d: common difference

4. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Find the indicated term of an arithmetic sequence. t 1 = 3; t n = t n – 1 + 4. 11.2 Arithmetic Sequences Find the twelfth term of the sequence in which t 12 = 3 + (12 – 1)4 = 47 t n = t 1 + (n – 1)d

5. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Find arithmetic means between two nonconsecutive terms. t 1 = 7, n = 5, and t 5 = 23 11.2 Arithmetic Sequences Find three arithmetic means between 7 and 23. t n = t 1 + (n – 1)d 23 = 7 + 4d d = 4

6. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Find arithmetic means between two nonconsecutive terms. t 1 = 7, n = 5, and t 5 = 23 11.2 Arithmetic Sequences Find three arithmetic means between 7 and 23. d = 4 7 + 4 = 11 11 + 4 = 15 15 + 4 = 19 arithmetic means: 11, 15, 19 TOC