Warm Up

L11-4 & L11-5 Obj: Students will be able to evaluate arithmetic and geometric series Use the sequence 5, 9, 13, 17, 21, 25, 29. Write the related series. Evaluate the series. 5 + 9 + 13 + 17 + 21 + 25 + 29 = 119 Related series Add to evaluate. The sum of the terms of the sequence is 119.

A staircase uses same-size cement blocks arranged 4 across, as shown below. Find the total number of blocks in the staircase.

 Use the summation notation to write the series 8 + 16 + 24 + . . . for 50 terms. 8 • 1 = 8, 8 • 2 = 16, 8 • 3 = 24, . . .   The explicit formula for the sequence is 8n. 8 + 16 + 24 + . . . + 400 = 8n The lower limit is 1 and the upper limit is 50.  50 n = 1

 Use the series (–2n + 3). a. Find the number of terms in the series. Arithmetic Series  4 n = 1 Use the series (–2n + 3). a. Find the number of terms in the series. b. Find the first and last terms in the series. c. Evaluate the series.

Practice

Use the formula to evaluate the series 5 + 15 + 45 + 135 + 405 + 1215. Geometric Series LESSON 11-5 Additional Examples Use the formula to evaluate the series 5 + 15 + 45 + 135 + 405 + 1215. The first term is 5, and there are six terms in the series. The common ratio is = = = = = 3 15 5 45 135 405 1215 So a1 = 5, r = 3, and n = 6. Sn = Write the formula. a1 (1 – r n) 1 – r = Substitute a1 = 5, r = 3, and n = 6. 5 (1 – 36) 1 – 3 = = 1820 Simplify. –3640 –2 The sum of the series is 1820.

Geometric Series Decide whether each infinite geometric series diverges or converges. Then determine whether the series has a sum.   n = 1 2 3 n a. b. 2 + 6 + 18 + . . . a1 = = , a2 = = 2 3 1 4 9 a1 = 2, a2 = 6 r = ÷ = 4 9 2 3 r = 6 ÷ 2 = 3 Since | r | < 1, the series converges, and the series has a sum. Since | r | 1, the series diverges, and the series does not have a sum. >

Homework: L11-4 (p632) #3-18t 19-24a 35-37a Homework: L11-4 (p632) #3-18t 19-24a 35-37a L11-5 (p 638 ) #3-27t 32-34a