Math 169
–
Sequences and Series Supplemental
Linear Growth and Arithmetic Sequence
Suppose that you earn $30 each day. If you start out with $100 in your savings, and you add
the $30 to your savings every evening, how much will you have saved after 11 days?
.
1

1

Examples
1)
4, 9, 14, 19, …
d
= 5
2)
12, 2, -8, -
18,…
d
= -10
The 20
th
term of the sequence is 12 + 19 (-10) = -178
The general term of the arithmetic sequence
a, a + d, a + 2d, a + 3d, … is
1
n
t
a
n
d
Examples
1)
Determine the 30
th
term of the arithmetic sequen
ce 4, 7, 10, …
t
30
= 4 + 29 (3) = 91
2)
Find the
n
th
term of the sequence 7, 2, -3, -
8,…
t
n
= 7 + (
n
–
1)(-5) = 12
–
5
n
The Sum of an Arithmetic Series
For the general arithmetic series
a
+ (
a
+
d
) + (
a
+ 2
d
) + …+
t
n
,
the sum of the first
n
terms is:
2
n
n
n
S
a
t
or
2
1
2
n
n
S
a
n
d
Examples
1.
Determine the sum of the first 30 terms of the arithmetic series 5 + 5.3 + 5.6 +…

Math 169
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