Arithmetic Sequences Lesson 30

Objectives HSF-BF.2: Write arithmetic sequences with an explicit formula, use them to model situations.

Arithmetic Sequence

Example; Arithmetic Sequence Find the 12th term of the arithmetic sequence 20, 14, 8, 2, 4, .... Step 1 Find the common difference: d = 14 – 20 = –6. Step 2 Evaluate by using the formula. an = a1 + (n – 1)d General rule. an = 20 + (n – 1)(-6) Substitute in a1 and d an = 20 + -6n + 6 Distribute an = -6n + 26 Simplify a12 = -6(12) + 26 Substitute 12 for n a12 = –46 The 12th term is –46.

Example; Arithmetic Sequence Find the 10th term of the arithmetic sequence 2, 14, 26, 38, 50, .... Step 1 Find the common difference: d = 14 – 2 = 12. Step 2 Evaluate by using the formula. an = a1 + (n – 1)d General rule. an = 2 + (n – 1)(12) Substitute in a1 and d an = 2 + 12n - 12 Distribute an = 12n - 10 Simplify a10 = 12(10) - 10 Substitute 10 for n a10 = 110 The 10th term is 110.

Example; Arithmetic Sequence Find the 11th term of the arithmetic sequence. -3, -5, -7, -9, … Step 1 Find the common difference: d = -5 – -3 = –2. Step 2 Evaluate by using the formula. an = a1 + (n – 1)d General rule. an = -3 + (n – 1)(-2) Substitute in a1 and d an = -3 + -2n + 2 Distribute an = -2n - 1 Simplify a11 = -2(11) - 1 Substitute 11 for n a11 = –23 The 11th term is –23.

Example; Arithmetic Sequence A small business sells $20,000 worth of sports memorabilia during its first year. The owner of the business has set a goal of increasing annual sales by $15,000 each year for 19 years. Assuming that this goal is met, find the total sales during the first 20 years this business is in operation. a1 = 20000 and d = 15,000 an = 20,000 + 15,000(n – 1) an = 15,000n + 5000. This implies that the 20th term of the sequence is a20 = 15,000(20) + 5000. a20 = 300,000 + 5000. a20 = 305,000. Total sales in the 20th year is $305,000.

#30: Arithmetic Sequences Questions? Summarize Notes Homework Google Classroom Quiz