Chapter 9 Coursepack:
Sequences, Series, and
Probability
Algebra 2
C. Bianchi, 2020
470
9.1 Introduction to Sequences
Objectives: Given the formula for a sequence, find the terms and a graph.
Given the terms in
...
Chapter 9 Coursepack:
Sequences, Series, and
Probability
Algebra 2
C. Bianchi, 2020
470
9.1 Introduction to Sequences
Objectives: Given the formula for a sequence, find the terms and a graph.
Given the terms in a sequence, find the formula.
A sequence is a list of numbers (called the terms of the sequence). The numbers typically
follow some sort of pattern. Here is an example of a sequence:
4 , 8 , 12 , 16 , 20 , 24 , …
first second third
term term term
The first term of the sequence is denoted
1
a
. The second term is called
2
a
, the third term is
called
3
a
, and so forth. In general, the n
th term in the sequence is called
n
a .
EXAMPLE 1: Find the first four terms of the sequence
n
a
= 3n + 8.
In order to find the first term,
1
a
, substitute 1 for n:
1
a
= 3(1) + 8 = 3 + 8 = 11.
The second term will be
2
a = 3(2) + 8 = 6 + 8 = 14.
The third term will be
3
a = 3(3) + 8 = 9 + 8 = 17.
The fourth term will be
4
a = 3(4) + 8 = 12 + 8 = 20.
The sequence is 11, 14, 17, 20, … This sequence can be graphed by using an n-axis and an
n
a -
axis. The graph would consist of a series of individual points representing each term in the
sequence. For example, the first term (
1
a
= 11) would be plotted as the point (1 , 11). The
second term (
2
a = 14) would be plotted as the point (2 , 14).
n
a
Notice that the points form a “linear” pattern. The
graph is not technically a line because the points on a
line would be connected. In this case, because the n
values can only be integers (representing the number 10
of the term), the graph will only consist of individual
points at n = 1, 2, 3, etc. Nonetheless, the points
would all fall on the line y = 3x + 8 , which would be
analogous to the sequence
n
a
= 3n + 8. n
[Show More]
.png)
