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

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

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 { … +97} S n is often called an n th partial sum, since it can represent the 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

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

Recognize partial sum notation and interpret its meaning Find partial sums of arithmetic and geometric sequences 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 S 4 is = 10 S 4 = 10

Let’s calculate another partial sum manually then confirm our answer using a calculator = 35 S 5 = 35

SWBAT… Recognize partial sum notation and interpret its meaning Find partial sums of arithmetic and geometric sequences Let’s calculate another partial sum manually then confirm our answer using a calculator = 35 S 5 = 35

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!

Precalculus 2; November 14 th, 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 PRACTICE wkst Geo Sequences word problems #s AND Geo Series 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

Geometric Sum Formula for Series Sum of the nth terms1 st term common ratio nth term Geometric Sequence VS. Geometric Series 1, 3, 9, 27, , -10, 20,5 + (-10) + 20

Find the sum of each geometric series. 1) …, n = 10 2) 2401 – – …, n = 5

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

Sum of an Infinite Geometric Series -1 < r < 1 Sum1 st termcommon ratio