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Write the next term in the series. Then write the series with summation notation.

Warm-Up. Write the next term in the series. Then write the series with summation notation. 5. n. 3n. -1. n=1. Objective: (1) Using and Writing Sequences (2) Using Series. Agenda: 4/02/15. 1.) Warm-up 2.) Questions: WS 11.1 Practice A #’s 1-27 ODD (Skip 11&13)

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Write the next term in the series. Then write the series with summation notation.

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  1. Warm-Up Write the next term in the series. Then write the series with summation notation. 5 n 3n -1 n=1

  2. Objective:(1) Using and Writing Sequences (2) Using Series Agenda: 4/02/15 1.) Warm-up 2.) Questions: WS 11.1 Practice A #’s 1-27 ODD (Skip 11&13) WS 11.1 Practice B #’s 1-25 ODD (Skip 11) 3.) Lesson: 11.2 Arithmetic Sequences and Series 4.) Class/Homework 5.) Work in Pairs/Groups STAY ON TASK!!

  3. 11.2 Arithmetic Sequences and Series (Day 1) In an Arithmetic Sequence, the differencebetween consecutive terms is constant. The constant difference is called the common differenceand is denoted by d. Ex. 1 Decide whether the sequence is arithmetic. Explain why or why not. - 3, 1, 5, 9, 13, … To decide whether a sequence is arithmetic, find the differences of consecutive terms. d = 1 – (- 3) = 4 d = 5 – 1 = 4 d = 9 – 5 = 4 d = 13 – 9 = 4 Each difference is 4, so the sequence is arithmetic.

  4. 11.2 Arithmetic Sequences and Series (Day 1) RULE FOR AN ARITHMETIC SEQUENCE Thenth term of an arithmetic sequence with first term a1 and common difference dis given by: an = a1 + (n – 1)d Ex. 2 Write a rule for the nth term of the arithmetic sequence. Then find a25. 50, 44, 38, 32, … a1 = 50 and d = 44 – 50 = - 6, so the sequence is arithmetic. A rule for thenth term is: Memorize!!

  5. 11.2 Arithmetic Sequences and Series (Day 1) Ex. 3 Write a rule for the nth term of the arithmetic sequence. d = 4, a14 = 46 In order to write the nth term the “d” and the “a1” ARE NEEDED. To find a1 use the a14 and the following rule. an = a1 + (n – 1)d a14 = a1 + (14 – 1)(4) 46 = a1 + 52 - 6 = a1 an = - 6 + (n – 1)(4) an = - 6 + 4n – 4 an = 4n – 10 Memorize!!

  6. 11.2 Arithmetic Sequences and Series (Day 1) Ex. 4 Write a rule for the nth term of the arithmetic sequence. a5 = 17, a15 = 77 In order to find the nth termWE NEED to find thea1 and the d. We use the a5 and the a15 terms in the nth term for an arithmetic sequence. an = a1 + (n – 1)d Memorize!!

  7. 11.2 Arithmetic Sequences and Series (Day 1)

  8. This is FUN!!!!! HOMEWORK Page 663 15 - 37 ALL

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