Download 10-2 Arithmetic Sequences and Series 4/13/16

April 13, 2016
10-2 Arithmetic Sequences and Series
4/13/16
April 13, 2016
Terminology and Notation
Series: 1 + 4 + 9 + 16
Partial Sum:
S1 =
S2 =
S3 =
S4 =
1, 3, 5, 7, 9, 11, . . .
Arithmetic Series: 7 + 10 + 13 + 16
n
k=
ƒ(x)
April 13, 2016
Find the sum of the integers from 1 to 100.
One Interesting Approach
1
100
2
99
3
98
4
97
5 . .
96
.
96
5
97
4
98
3
Derive a formula for the sum of an arithmetic sequence.
99
2
100
1
April 13, 2016
Derive the alternate formula.
A theater has 60 seats in the first row, 68 seats in the second row, 76 seats in the third row, and
so on in the same increasing pattern. If the theater has 20 rows of seats, how many seats are in
the theatre?
April 13, 2016
Examples:
Find the sum of each arithmetic series.
1. The fist 50 odd numbers
2. the first 250 even numbers
3. a1 = 20, d = 7, n = 30
Determine the number of terms n in each arithmetic series.
a1 = 19, an = 118, Sn = 822
April 13, 2016
Examples:
Find the first three terms of each arithmetic series.
1. n = 35, an = 173, Sn = 3080
Find the sum..
2. a1 = 5, an = 68, Sn = 365
April 13, 2016
Practice
A student borrowed $4000 for college expenses. The loan was repaid over a 100-month
period, with monthly payments as follows:
$60.00, $59.80, $59.60, . . . , $40.20.
How much did the student pay over the life of the loan? How much interest was paid?
Find the sum of each arithmetic series.
1. The fist 75 odd numbers
2. a1 = 8, d = –3, n = 16
April 13, 2016
Practice
Find the first three terms of each arithmetic series.
1. n = 45, an = 126, Sn = 2700
2. a1 = 19, an = 96, Sn = 690
Determine the number of terms n in each arithmetic series.
a1 = 16, an = 163, Sn = 4475
Find the sum of the arithmetic sequence.
April 13, 2016