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!!
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 + … + 8
1
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
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.
A closer look at geometric seriesSn = 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.r
rtS
n
n
1
)1(1
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 + rtn-1, where Sn-1 is the previous
sum and rtn-1 = tn since series is geometric.
r
rtS
n
n
1
)1(1
Ex 3 Identify t1, r and n, then evaluate the series.
c. d.
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
