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Lesson 13 – 3 Arithmetic & Geometric Series

Pg 695 #1–11odd, 17–18, 22, 24, 25, 27, 32, 36, 37. Lesson 13 – 3 Arithmetic & Geometric Series. Pre-calculus. Objective: - Find sum of part of the sequence  - use formulas. S eries The sum of the terms of a sequence. - Can be finite or infinite.

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Lesson 13 – 3 Arithmetic & Geometric Series

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  1. Pg 695 #1–11odd, 17–18, 22, 24, 25, 27, 32, 36, 37 Lesson 13 – 3Arithmetic & Geometric Series Pre-calculus Objective: - Find sum of part of the sequence  - use formulas

  2. Series • The sum of the terms of a sequence. • - Can be finite or infinite. • - We often utilize sigma notation to denote a series • is the greek letter sigma – stands for “sum” • Ex 1) Express 3 – 6 + 9 – 12 + 15 using sigma notation • - five terms • - alternating signs • - rule 3k • Ex 2) Find the following sums. • a) b) index sequence rule = 140

  3. is an infinite series. The sum of the first n terms is called the nth partial sum of the series and is denoted by Sn. Ex 3) Find the indicated partial sum. a) S10 for –3 – 6 – 9 – 12 – 15 – 18 – 21 – 24 – 27 – 30 = –165 b) S6 for keep going… = 4 + 14 + 24 + 34 + 44 + 54 = 174 • Writing out all these terms is cumbersome! We have formulas! • The sum of the arithmetic series. • If a1, a2, a3, … is an arithmetic sequence with common difference d • an = a1 + (n – 1)d • Which should you use? Discuss advantages of each! or

  4. Talk to Partner What's a series? What are the two formulas for finding partial sum? What symbol (Greek letter) do we use to denote SUM?

  5. Ex 4) Find the indicated partial sum. a) S8 for 15, 9, 3, –3, … use b) S24 for use We can also use a formula for the sum of a geometric series. If a1, a2, a3, … is a geometric sequence with common ratio r an = a1rn–1 = 306 a24 = 1.5(24) – 6 = 30 a1 = 1.5(1) – 6 = -4.5 Ex 5) Find the partial sum S7 for the series 1 – 0.8 + 0.64 – 0.512 + … Be careful! Watch order of operations!

  6. Ex 6) Marc’s grandmother gives him $100 on his birthday every year beginning with his third birthday. It is deposited in an account that earns 7.5% interest compounded annually. a1 = 100 r = 1.075 (why the 1??) How much is the account worth the day after Marc’s 10th birthday?

  7. Talk to Partner Difference between Arithmetic vs geometric series (conceptual)? Formula for geometric series? Watch out for what?

  8. Homework Pg 695 #1–11odd, 17–18, 22, 24, 25, 27, 32, 36, 37

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