Today’s Vocab:Today’s Agenda Sigma

Partial SumInfinite SeriesFinite Series

HW: Worksheet14-2b Arithmetic and Geometric Sequences

AND QUIZ corrections!!!

1. Do Now: take out Quiz #1 from Unit 22. Sequence vs. Series: what do you

know? Think, pair, share

PRECALCULUS 2

2. CW: Vocab ReviewSigma 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 {1 + 3 + 5 + … +97}

Sn is 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

B

nn A

a

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?n Sum whatever appears after the

SigmaIn this case, we are summing n

And what is the value of n? 4

1n

n The values are shown below and above

the SigmaWe sum values of n from 1 to 4

S4 is4

1n

n 1 + 2 + 3 + 4 = 10 S4 =

10

Let’s calculate another partial sum manually then confirm our answer using a calculator

5

1

2 1n

n

3 + 5 + 7 + 9 + 11 = 35

S5 = 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

5

1

2 1n

n

3 + 5 + 7 + 9 + 11 = 35

S5 = 35

On the Calculator!2nd stat - - go to MATH, pick 5. sum2nd stat – OPS pick 5. SeqThen type in:(3x+2, x, 2, 5))

Try examples on board!

Precalculus 2; November 14th, 2011DO 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 wkst Geo Sequences word problems #s 29-31 AND Geo Series 13-22 ALL and 27 & 28

1,1

)1(1

rr

raS

n

n

Explain WHY in the GEOMETRIC SERIES EQUATION ABOVE, WHY can “r” not equal “1”.

If done, please complete vocabulary match-up.

CW: Geometric FINITE SeriesGeometric INFINITE Series

Geometric Sum Formula for Series

Sum of the nth terms 1st term common ratio nth term

Geometric Sequence VS. Geometric Series1, 3, 9, 27, 81 1 + 3 + 9 + 27 + 81

5, -10, 20, 5 + (-10) + 20

1,1

)1(1

rr

raS

n

n

Find the sum of each geometric series.

1) 7 + 21 + 63 + …, n = 10

2) 2401 – 343 + 49 – …, n = 5

1,1

)1(1

rr

raS

n

n

Find the sum of each geometric series.

3)

4)

7,2

1,161 nra

2,384,31 naa n

1,1

)1(1

rr

raS

n

n

Sum of an Infinite Geometric Series-1 < r < 1

Sum 1st term common ratio

r

aS

1

1