Algebra II- Chapter 9 Day #1
Topic: Mathematical Patterns- Identifying the Difference
Between Arithmetic and Geometric Sequences.
Today, we will learn how to identify mathematical patterns
found in a sequence. Finding this mathematical pattern will help
us determine the difference between arithmetic sequences and
geometric sequences. We will also learn how to use formulas to
find the “nth” term of a sequence.
STANDARDS/GOALS:
A.SSE.4:


I can identify whether a
sequence is arithmetic or
geometric.
I can use a given formula to
determine “nth” terms of a
sequence.
Arithmetic Sequence is a sequence of numbers such that the difference between
the consecutive terms is constant. This constant is called the common difference.
The explicit formula for an arithmetic sequence is 𝑎𝑛 = 𝑎1 + 𝑑(𝑛 − 1). In this
formula, 𝑎1 is the first term of the sequence and d is the common difference.
Geometric Sequence, is a sequence of numbers where each term after the first is
found by multiplying the previous one by a fixed, non-zero number called the
common ratio. The explicit formula for a geometric sequence is 𝑎𝑛 =𝑎1 ∗ 𝑟 𝑛−1 . In
this formula, 𝑎1 is the first term of the sequence and r is the common ratio.
In both cases, 𝑎𝑛 represents the last term of the sequence and n represents the
number of terms in the sequence.
Examples: Identify each sequence as arithmetic, geometric, or
neither. Explain.
1. 1,6,11,16,….
2. 125, 62.5, 31.25, 15.625, ….
3. 1, 5, 10, 16,…
4. -5, 5, -5, 5, ……
Examples: Determine the “nth” term of each sequence.
𝑎𝑛 = 3 ∗ 2𝑛−1 , 𝑎10
1.
𝑎𝑛 = 3𝑛 − 5 , 𝑎25
2.
3.
𝑎𝑛 = 2𝑛 + 2, 𝑎15
4. 𝑎𝑛 = 4 ∗ ( )
2
1 𝑛−1
, 𝑎5
Examples: Describe the mathematical pattern and find the next
3 terms in the sequence.
1. 3,6,12,24,48
2. 1, 3, 9, 27, 81
3. 6, 9, 12, 15, 18,
4. 9, 11, 13, 15,
Homework – Chapter 9 Day #1 (mathematical patterns)
Find the first 6 terms of each sequence and determine
whether the sequence is arithmetic or geometric.
1.
2. 𝑎𝑛 = 2 ∗ 2𝑛−1
𝑎𝑛 = −2𝑛 + 1
3 𝑛−1
4. 𝑎𝑛 = 7 ∗ ( )
4
1
1 𝑛−1
5. 𝑎𝑛 = ( ) ∗ ( )
2
4
3. 𝑎𝑛 = 8𝑛 + 2
6. 𝑎𝑛 = 3𝑛 + 5
Find 𝑎5, 𝑎50 , 𝑎𝑛𝑑 𝑎100 for the following sequences.
3 𝑛−1
. 𝑎𝑛 = 6 ∗ ( )
4
8. . 𝑎𝑛 = 5 ∗ (2)𝑛−1
9. 𝑎𝑛 = −2𝑛 + 1
10. 𝑎𝑛 = −5𝑛 − 11
7.