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Good Morning!! Sharpen pencils for your quiz and get your calculators!!

Good Morning!! Sharpen pencils for your quiz and get your calculators!!. Prepare for your quiz (20 min.) Complete warm-up activity (6 min.) when finished with quiz!!. You have 20 minutes to complete your quiz!!. No talking! Eyes on your own paper!! Show your work for full credit!!.

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Good Morning!! Sharpen pencils for your quiz and get your calculators!!

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  1. Good Morning!! Sharpen pencils for your quiz and get your calculators!! Prepare for your quiz (20 min.) Complete warm-up activity (6 min.) when finished with quiz!!

  2. You have 20 minutes to complete your quiz!! • No talking! • Eyes on your own paper!! • Show your work for full credit!!

  3. Warm-up (6 minutes) Evaluate each series shown below. Add a few more terms to each series. Describe what you notice about the sum as you add more terms. 1. 595 + 495 + 395 + 295 2. 210 + 160 + 110 + 60 + 10 – 60 3. 3 + 9 + 27 + 81 4. 4 + 2 + 1 + … +

  4. Geometric Series What You’ll Learn • To evaluate a finite geometric series • To express a geometric series in summation notation • To evaluate a finite geometric series in summation notation

  5. Definition • A geometric series is the expression for the sum of the terms of a geometric sequence. Note: A geometric sequence has a common ratio, r, between each pair of consecutive terms. • As with arithmetic series, you can use a formula to evaluate a finite geometric series.

  6. A closer look at geometric series Sn = t1 + t2 + t3 + … + tn (sum of n terms) Each term of a geometric series can be found using tn = t1rn-1. Therefore, Sn = t1 + t1r + t1r2 + … t1rn-1 rSn = t1r + t1r2 + t1r3+ …t1rn Multiplying by r Sn – rSn = t1 – t1rn Subtracting these 2 equations Sn(1– r) = t1(1– rn) Factoring out common terms Solving for Sn.

  7. Formulas for Finite Geometric Series Explicit form Sn is the sum of the n terms t1 is the 1st term and r is the common ratio. Recursive formula S0 = 0 Sn = Sn-1 + rtn-1, where Sn-1 is the previous sum and rtn-1 = tn since series is geometric.

  8. c. d. Ex 3 Identify t1, r and n, then evaluate the series.

  9. Tonight’s Assignment • Complete handouts on Arithmetic and Geometric Series • Do only the multiples of 3 on both pages • Begin reviewing for Final Exam • Exemptions will be stated after the last test next week

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