Download 11.2 – Arithmetic Sequences

Arithmetic Series/Geometric
Series
Review
Sum of a Finite Arithmetic Series
n
Sn  ( a1  an )
2
Where: Sn is the sum of all the terms
n = number of terms
a1 = first term
an = last term
Problem 1:
• Find the sum of the following series:
2, 11, 20, 29, 38, 47
Problem 2:
• A 20-row movie theatre has three sections
of seating. In each section, the number of
seats in a row increases by one with each
successive row. The first row of the
middle section has 10 seats. The front
row of each of the two side sections has 4
seats. Find the total number of chairs in
each section. Then find the overall total
number of chairs.
Formula for the Sum of a Finite
Geometric Series
1 r
S n  a1 
1

r

n
n = # of terms
a1 = 1st term
r = common ratio



Problem 1:
• Find the sum of the following series:
3, 6, 12, …. 96
Problem 2:
• In March, the Floyd family stars saving for
a vacation at the end of August. The
Floyds expect to the vacation to cost
$1375. They start with $125. Each month
they will deposit 20% more than the
previous month. Will they have enough
money for their trip?
Summation
When we don’t want to write out a whole bunch of numbers in the series, the
summation symbol is used when writing a series. The limits are the greatest
and least values of n.
Upper Limit (greatest value of n)
Summation symbol
Explicit function for
the sequence
Lower Limit (least value of n)
So, the way this works is plug in n=1 to the equation and continue through n=3.
(5*1 + 1) + (5*2 +1) + (5*3 + 1) = 33
Writing a series in summation form
• Ex: 102 + 104 + 106 + 108 + 110 + 112
n = 6 terms
1st term = 1
Rule: Hmmmm. . . .
Rule = 100 + 2n
Let’s Evaluate:
Sn 
n
( a1  an )
2
Yes, you can add manually. But let’s try
using the shortcut:
Sn 
6
(102  112)  642
2
Let’s try some
Find the number of terms, the first term and the last term.
Then evaluate the series:
Let’s try some
Find the number of terms, the first
term and the last term. Then
evaluate the series:
Why is the
answer not 58?
N = 10
1st = 1
Notice we can use the
shortcut here:
Last = 10
a1= 1-3 = -2
N=4
1st = 2
Last = 5
a10 = 10-3 = 7
4+9+16+25 = 54
Sn 
10
( 2  7)  5(5)  25
2
Note: this is
NOT an
arithmetic
series. You can
NOT use the
shortcut; you
have to
manually
crunch out all
the values.