Download Geometric Sequence

Today’s Agenda
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
"The summation from 1 to 4 of 3n":
Today’s Vocab:
Sigma
Partial Sum
Infinite Series
Finite Series
HW: Worksheet14-2b
Arithmetic and
Geometric Sequences
AND QUIZ corrections!!!
SWBAT…  Recognize partial sum notation and interpret its meaning
 Find partial sums of arithmetic and geometric sequences
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
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)
B
SIGMA
(SUM OF TERMS)
a
n
n A
NTH TERM
(SEQUENCE)
LOWER BOUND
(NUMBER)
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
n In this case, we are summing n

And what is the value of n?
4
n
n 1
S4 is
The values are shown below and above the Sigma
We sum values of n from 1 to 4
4
n
n 1
1 + 2 + 3 + 4 = 10
S4 = 10
 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
 2n  1
n 1
3 + 5 + 7 + 9 + 11 = 35
S5 = 35
Let’s calculate another partial sum manually then confirm
our answer using a calculator
5
 2n  1
3 + 5 + 7 + 9 + 11 = 35
n 1
SWBAT…  Recognize partial sum notation and interpret its meaning
 Find partial sums of arithmetic and geometric sequences
S5 = 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 14th, 2011
DO NOW (5-7 min):
Take out HW, then:
We will
a1 (1  r )
Sn 
,r 1
1 r
using SIGMA NOTATION
 Evaluate the SUM of a FINITE
geometric sequence and an INFINTIE
Geometric Sequence!
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 Series
Geometric INFINITE Series
 Evaluate the SUM of a SEQUENCE
ANNOUNCEMENT: QUIZ THURSDAYGEOMETRIC 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
Geometric Sum Formula for Series
a1 (1  r n )
Sn 
,r 1
1 r
Sum of the nth terms
Geometric Sequence
1, 3, 9, 27, 81
5, -10, 20,
1st term
VS.
common ratio
nth term
Geometric Series
1 + 3 + 9 + 27 + 81
5 + (-10) + 20
Find the sum of each geometric series.
1) 7 + 21 + 63 + …, n = 10
2) 2401 – 343 + 49 – …, n = 5
a1 (1  r n )
Sn 
,r 1
1 r
Find the sum of each geometric series.
3) a  16, r  1 , n  7
1
2
4) a1  3, an  384, n  2
a1 (1  r n )
Sn 
,r 1
1 r
Sum of an Infinite Geometric Series
-1 < r < 1
a1
S
1 r
Sum
1st term
common ratio