Today’s Vocab :

1. Precalculus 2 Today’s Agenda Sigma Partial Sum Infinite Series Finite Series HW: Worksheet14-2b Arithmetic and Geometric Sequences AND QUIZ corrections!!! • Do Now: take out Quiz #1 from Unit 2 • Sequence vs. Series: what do you know? Think, pair, share • CW: Vocab Review • Sigma Notation and the calculator! Today’s Vocab: • CW2: Exploration 14-3a: Introduction to Series "The summation from 1 to 4 of 3n":

2. Sequence vs. Series; Think Pair Share OUT! • Sequence: • Series:

3. Vocabulary • Arithmetic Sequence- each term after the first is found by adding a constant, called the common difference, d, to the previous term • Geometric Sequence – each term after the first is found by MULTIPLYING a constant, called the common ratio, r, to get the next term • Sequence- a set of numbers {1, 3, 5, 7, …} • Terms- each number in a squence • Common Difference- the number added to find the next term of an arithmetic sequence • Common Ratio - number multiplied to find the next term of an geometric sequence • Arithmetic Series- the sum of an arithmetic sequence • Series- the sum of the terms of a sequence {1 + 3 + 5 + … +97} Snis often called an nth partial sum, since it can representthe sum of a certain "part" of a sequence. Sigma Notation – A series can be represented in a compact form,called summation notation, or sigma notation.The Greek capital letter sigma, , is used to indicate a sum. Geometric Series- the sum of an geometric sequence

4. UPPER BOUND (NUMBER) SIGMA (SUM OF TERMS) NTH TERM (SEQUENCE) LOWER BOUND (NUMBER)

5. Partial Sums are written with a (Sigma) meaning SUM or “add them all up” So what are we summing? Sum whatever appears after the Sigma In this case, we are summing n And what is the value of n? The values are shown below and above the Sigma We sum values of n from 1 to 4 S4= 10 S4is 1 + 2 + 3 + 4 = 10

6. Let’s calculate another partial sum manually then confirm our answer using a calculator S5= 35 3 + 5 + 7 + 9 + 11 = 35

7. Let’s calculate another partial sum manually then confirm our answer using a calculator S5= 35 3 + 5 + 7 + 9 + 11 = 35

8. On the Calculator! • 2nd stat - - go to MATH, pick 5. sum • 2nd stat – OPS pick 5. Seq • Then type in: • (3x+2, x, 2, 5)) • Try examples on board!

9. Precalculus 2; November 14th, 2011 DO NOW (5-7 min): Take out HW, then: We will • Evaluate the SUM of a SEQUENCE using SIGMA NOTATION • Evaluate the SUM of a FINITE geometric sequence and an INFINTIE Geometric Sequence! ANNOUNCEMENT: QUIZ THURSDAY-GEOMETRIC SERIES AND SIGMA NOTATION!! • HW: ch. 11-3 PRACTICE wkstGeo Sequences word problems #s 29-31 AND Geo Series 13-22 ALL and 27 & 28 Explain WHY in the GEOMETRIC SERIES EQUATION ABOVE, WHY can “r” not equal “1”. If done, please complete vocabulary match-up. CW: Geometric FINITE Series Geometric INFINITE Series

10. Geometric Sum Formula for Series Sum of the nth terms 1st term common ratio nth term Geometric Sequence VS. Geometric Series 1, 3, 9, 27, 81 1 + 3 + 9 + 27 + 81 5, -10, 20, 5 + (-10) + 20

11. Find the sum of each geometric series. • 7 + 21 + 63 + …, n = 10 • 2401 – 343 + 49 – …, n = 5

12. Find the sum of each geometric series. 3) 4)

13. Sum of an Infinite Geometric Series -1 < r < 1 Sum 1st term common ratio