12 3 Arithmetic Sequences and Series LEARNING GOALS

12 -3 Arithmetic Sequences and Series LEARNING GOALS FOR LESSON 12. 3. 1 Determine if a sequence is arithmetic. Is so, find the common first difference and the next term 12. 3. 2 Find the nth term of an arithmetic sequence 12. 3. 3 Find the missing terms of an arithmetic sequence 12. 3. 4 Find the sum of an arithmetic sequence ARITHMETIC SEQUENCE: LG 12. 3. 1 Determine whether the sequence could be arithmetic. If so, find the common first difference and the next term. A. – 10, – 4, 2, 8, 14, … C. B. – 2, – 5, – 11, – 20, – 32, …

12 -3 Arithmetic Sequences and Series Ex. 2: Finding the nth Term Given an Arithmetic Sequence A. Find the 12 th term of the arithmetic sequence 20, 14, 8, 2, -4, . . LG 12. 3. 2 Step 1 Find the common difference. Step 2 Evaluate by using the formula. B. Find the 11 th term of the arithmetic sequence. – 3, – 5, – 7, – 9, … Ex. 3 A: Finding the nth Term Given Two Terms LG 12. 3. 3 Find the 5 th term of the arithmetic sequence with a 3 = 20. 5 and a 8 = 13 Step 1 Find the common difference. Step 2 Find a 1. Step 3 Write a rule for the sequence, and evaluate to find a 5.

12 -3 Arithmetic Sequences and Series Ex. 3 B: Finding the nth Term Given Two Terms Find the 11 th term of the arithmetic sequence. LG 12. 3. 3 a 2 = – 133 and a 3 = – 121 In Lesson 12: 2 you wrote and evaluated series. An Arithmetic Series is the indicated sum of the terms of an arithmetic sequence. Ex. 4: Finding the nth Term Given an Arithmetic Sequence Find the indicated sum for each arithmetic series A. S 15 + 12 + (-1) + (-14) +. . . B. LG 12. 3. 4