Use the table to write an equation. 1. Warm Up Use the table to write an equation. 1. 2. 3. x 1 2 3 4 y 5 10 15 20 y = 5x x 1 2 3 4 y –2.5 –5 –7.5 –10 y = –2.5x x 1 2 3 4 y 5 8 11 14 y = 3x + 2

Learn to identify and evaluate arithmetic sequences.

Vocabulary sequence term arithmetic sequence common difference

A sequence is an ordered list of numbers or objects, called terms A sequence is an ordered list of numbers or objects, called terms. In an arithmetic sequence, the difference between one term and the next is always the same. This difference is called the common difference. The common difference is added to each term to get the next term.

Find the common difference in each arithmetic sequence. Additional Example 1: Finding the Common Difference in an Arithmetic Sequence Find the common difference in each arithmetic sequence. A. 11, 9, 7, 5, … 11, 9, 7, 5, … The terms decrease by 2. –2 –2 –2 The common difference is -2. B. 2.5, 3.75, 5, 6.25, … 2.5, 3.75, 5, 6.25, … The terms increase by 1.25. +1.25 +1.25 +1.25 The common difference is 1.25.

Find the common difference in each arithmetic sequence. Check It Out: Example 1 Find the common difference in each arithmetic sequence. A. 2, 6, 10, 14, … 2, 6, 10, 14, … The terms increase by 4. +4 +4 +4 The common difference is 4. B. 2.5, 5, 7.5, 10, … 2.5, 5, 7.5, 10, … The terms increase by 2.5. +2.5 +2.5 +2.5 The common difference is 2.5.

Additional Example 2: Finding Missing Terms in an Arithmetic Sequence Find the next three terms in the arithmetic sequence –8, –3, 2, 7, ... Each term is 5 more than the previous term. 7 + 5 = 12 Use the common difference to find the next three terms. 12 + 5 = 17 17 + 5 = 22 The next three terms are 12, 17, and 22.

Check It Out: Example 2 Find the next three terms in the arithmetic sequence –9, –6, –3, 0, ... Each term is 3 more than the previous term. 0 + 3 = 3 Use the common difference to find the next three terms. 3 + 3 = 6 6 + 3 = 9 The next three terms are 3, 6, and 9.

Additional Example 3A: Identifying Functions in Arithmetic Sequences Find a function that describes each arithmetic sequence. 6, 12, 18, 24, … n n • 6 y 1 2 3 4 1 • 6 6 Multiply n by 6. 2 • 6 12 3 • 6 18 y = 6n 4 • 6 24 n • 6 6n

Additional Example 3B: Identifying Functions in Arithmetic Sequences Find a function that describes each arithmetic sequence. –4, –8, –12, –16, … n n • (– 4) y 1 2 3 4 1 • (–4) –4 Multiply n by -4. 2 • (–4) –8 3 • (–4) –12 y = –4n 4 • (–4) –16 n • (–4) –4n

Check It Out: Example 3A Find a function that describes each arithmetic sequence. 3, 6, 9, 12, … n n • 3 y 1 2 3 4 1 • 3 3 Multiply n by 3. 2 • 3 6 3 • 3 9 y = 3n 4 • 3 12 n • 3 3n

Check It Out: Example 3B Find a function that describes each arithmetic sequence. –7, –14, –21, –28, … n n • (-7) y 1 2 3 4 1 • (-7) -7 Multiply n by -7. 2 • (-7) -14 3 • (-7) -21 y = -7n 4 • (-7) -28 n • (-7) -7n

Lesson Quiz: Part 1 Find the common difference in each arithmetic sequence. 1. 4, 2, 0, –2, … –2 4 3 8 3 10 3 2 3 2. , 2, , , … Find the next three terms in each arithmetic sequence. 3. 18, 13, 8, 3, … 4. 3.6, 5, 6.4, 7.8, … –2, –7, –12 9.2, 10.6, 12

Lesson Quiz: Part 2 Find a function that describes the arithmetic sequence. 5. –5, –10, –15, –20, … Possible Answer: y = –5x 6. –1, 2, 5, 8, … Possible Answer: y = 3x – 4