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