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Lesson Overview 12-4A

Lesson Overview 12-4A. 5-Minute Check Lesson 12-5A. 5-Minute Check Lesson 12-5B. Math ador Gameplan. Section 12.5: Sigma notation and the nth term CA Standards: MA 5.2 Daily Objective (5/28/13):

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Lesson Overview 12-4A

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  1. Lesson Overview 12-4A

  2. 5-Minute Check Lesson 12-5A

  3. 5-Minute Check Lesson 12-5B

  4. MathadorGameplan Section 12.5:Sigma notation and the nth term CA Standards: MA 5.2 Daily Objective (5/28/13): Students will be able to write expanded form of a sigma notation and express a series using a sigma notation. Homework:page 798 (#14 to 44, 48) due Thursday!

  5. Examples • Examples of Series • Arithmetic: 1 + 8 + 15 + 22 + 29 • Geometric: -8 + 2 – 1/2 + 1/8 - … • There is another way to write these series Summation Notation

  6. Summation Notationaka Sigma Notation • Σis the Greek Letter “sigma” • n = 1 is the starting value of n • k is the maximum value of n • an is the nth term formula

  7. Express the arithmetic series in summation notation 1 + 8 + 15 + 22 + 29 Find the nth term formula an = a1 + (n – 1)d an = 1 + (n – 1)7 = 7n – 6 Summation Notation Back to our examples

  8. Back to our examples • Express the Geometric series in sigma notation -8 + 2 – 1/2 + 1/8 - … • Find the nth term formula • an = a1 r(n-1) • an = -8(-1/4)(n-1) • Sigma Notation

  9. Lesson Overview 12-5A

  10. Time to work • Expand the series

  11. Lesson Overview 12-5C

  12. Time to Work • Write the series in summation notation • 2+6+18+54+… • Geometric • an = a1r(n-1) • r = 3 a1 = 2 • an = 2(3)(n-1)

  13. Example • Expand and evaluate the sum: a) b) • Solution: • a) (12 + 1) + (22 + 1) + (32 + 1) + (42 + 1)+ (52 + 1) + (62 + 1) • = 2 + 5 + 10 + 17 + 26 + 37 • = 97 • b) [(-2)4 – 5] + [(-2)5 – 5] + [(-2)6 – 5] + [(-2)7 – 5] • = [16 – 5] + [-32 – 5] + [64 – 5] + [-128 – 5] • = 11 – 37 + 59 – 133 = -100

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