1. Warm Up

2. 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.
= 119
Related series
Add to evaluate.
The sum of the terms of the sequence is 119.

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

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

6.  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.

7. Practice

9. 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
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.

11. 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
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.
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15. 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 a