Notes 9.4 Series.notebook
April 17, 2015
Bellwork
Find the sum: 1 + 2 + 3 + ... + 98 + 99 + 100
Notes 9.4 Series.notebook
April 17, 2015
Notes 9.4: Series of Arithmetic and Geometric Sequences
Sequence ­ list of ordered numbers
Series ­ finite SUM of a sequence
Notes 9.4 Series.notebook
April 17, 2015
Arithmetic Series
Given a finite arithmetic series: a1 + a2 + a3 + ...+ an
then
n = # of terms
a1 = first term
an = nth term (last term)
WHY??? Check this out!
Notes 9.4 Series.notebook
Find the sum of the arithmetic sequence.
1. 4, 6, 8, 10, ... Find the sum of the first 20 terms.
2. Find the 15th partial sum given a1 = 8 and a15 = ­48.
3. Find the 50th partial sum given the arithmetic sequence an = 2n ­ 1.
April 17, 2015
Notes 9.4 Series.notebook
Now what about these tricky ones?
4. What is the sum of the series 2 + 4 + 6 + ... + 100?
5. Find n given Sn = ­1110 and the sequence ­8, ­10, ­12, ­14, ...
April 17, 2015
Notes 9.4 Series.notebook
April 17, 2015
Now what about these tricky ones?
6. What is the sum of the series 7 + 11 + 15 + ... + 203 + 207?
7. Find n given Sn = 60 and the sequence 6, 9, 12, ...
Notes 9.4 Series.notebook
April 17, 2015
Geometric Series
Given a finite geometric series: a1 + a1r + a1r2 + ...+ a1rn­1
then
n = # of terms
a1 = first term
r = common ratio
Notes 9.4 Series.notebook
http://www.mathalino.com/reviewer/derivation­of­formulas/sum­of­finite­and­
infinite­geometric­progression
April 17, 2015
Notes 9.4 Series.notebook
April 17, 2015
Find the sum of the geometric series.
8. 32, 16, 8, 4, ... Find the sum of the first 15 terms.
9. Find the sum of the first 9 terms.
Notes 9.4 Series.notebook
Now what about these tricky ones?
10. What is the sum of the series 3 + 6 + 12 + 24 + ... + 3072?
11. What is the sum of the series 4 + 12 + 36 + 108 + ... + 972?
April 17, 2015
Notes 9.4 Series.notebook
April 17, 2015
12. A soldier rescues his king in battle. The king grants the soldier any prize "within reason" form the riches of the kingdom. The soldier asks for a chessboard with a single kernel of wheat on the first square, two kernels of wheat on the second square, then four, then eight, and so on for all 64 squares of the chessboard. How many total kernels of wheat is the soldier requesting? Describe the domain and range of this situation.
Notes 9.4 Series.notebook
April 17, 2015
Now, find the sum. Watch out for arithmetic vs. geometric!!!
13. ­5, 25, ­125, 625, ...; n = 9 14. ­5, ­10, ­15, ­20, ...; n = 12 15. 16. ; n = 11 ; n = 10