9_1GN_ Sequences as Functions
Name ___________________________
Arithmetic Sequence: a sequence where each term is determined by adding a constant value to the previous
term.
This constant value is called the ______________________________________________.
It is denoted by the variable _______.
Geometric Sequence: a sequence where each term is determined by multiplying a nonzero constant by the
previous term.
The nonzero constant value if called the ________________________________________.
It is denoted by the variable________.
Determine if the sequence is arithmetic. What is the common difference? Write the next three terms for each.
Determine if the sequence is Geometric. What is the common ratio? Write the next three terms for each.
Consider each of the following sequences. Determine if it is arithmetic or geometric, Find the common difference or ratio,
and then Graph each sequence.
2, 4,8,...
Describe the type/family of graph in 1:
Describe the type/family of graph in 2:
Arithmetic Sequences and Series
Common Difference (d)
𝒅 = 𝒂𝒏+𝟏 − 𝒂𝒏
The nth Term of an Arithmetic Sequences
𝒂𝒏 = 𝒂𝟏 + (𝒏 − 𝟏)𝒅 ; 𝑤ℎ𝑒𝑟𝑒 𝒂𝟏 = 𝑡ℎ𝑒 1𝑠𝑡 𝑡𝑒𝑟𝑚
𝒅 = 𝑐𝑜𝑚𝑚𝑜𝑛 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒
𝒏 = 𝑎𝑛𝑦 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑖𝑛𝑡𝑒𝑔𝑒𝑟
Ex 1. Use the formula for the nth term to find the 13th term of the arithmetic sequence with
the first term of 21 and a common difference of −6
Practice:
1a. Find the 7th term of the arithmetic
sequence with 𝑎1 = 15 𝑎𝑛𝑑 𝑑 = 4
1b. Find the indicated term the arithmetic
sequence. 𝑎1 = −18, 𝑑 = 12, 𝑛 = 16
Ex 2. Find 𝑎31 of the arithmetic sequence 18 , 15 , 12 , 9 …
Practice: Find the indicated term for the given arithmetic sequence given below.
2a. Find 𝑎15 , −5, −12, −19, …
2b. Find 𝑎100 , −63 , −58 , −53 , −48 …
Ex 3. Write an equation for the nth term of the arithmetic sequence: −14 , −5 , 4 , 13 …
Practice: Write an equation for the nth term of each arithmetic sequence.
3a. 𝑎1 = 72 , 𝑑 = −13
3b. −56 , −39 , −22 , −5 …
Definition: Arithmetic Means are the terms between any two nonconsecutive terms of an arithmetic
sequence.
Ex 4. Find the arithmetic means in the sequence
−8 , ______, ______, ______, _____,22
4a. Find the arithmetic means in the sequence
24 , ______, ______, ______,4
A SERIES is formed when the terms of a sequence are added. An arithmetic series is the sum of the
terms of an arithmetic sequence.
𝒏
The sum 𝑆𝑛 of the first n terms of an arithmetic series is given by the formula 𝑺𝒏 = (𝒂𝟏 + 𝒂𝒏 )
𝟐
Ex 5. Find the sum of each arithmetic series; −18 + (−15) + (−12) + ⋯ + 66
5a. Find the sum of each arithmetic series;
2 , 4 , 6 , + ⋯ + 100
5b. Find the sum: 𝑛 = 19, 𝑎𝑛 = 154, 𝑑 = 8
The Greek letter, Sigma (Σ) is used to denote the sum of a series.
Find the sum of each arithmetic series.
6.
16
7.
18
∑(4𝑘 − 2)
∑ 6𝑘 − 1
𝑘=1
𝑘=5
9_1HW_Arithmetic Sequences and Series
Algebra II
Name_________________________________
1. Which of the following sequences are arithmetic? Which are Geometric? Which are neither? Justify your
answers. State the next 2 terms in the arithmetic or geometric sequence.
a) 0.125, -0.5, 2, …
b) 18, 12, 8, …
c) 64, 48, 36, …
d) 81, 108, 144
e) 1/3, 1, 3, 9,…
2. Find the 16th term of an arithmetic sequence with
the first term equal to -18 and a common difference
of 12.
3. Write a general equation for the nth term of the
arithmetic sequence 24, 35, 46, …
4. Find the arithmetic means in the sequence
– 2, 6, ______, ______, ______, ______, 49.
5. Find the sum of an arithmetic series with 19 terms,
a common difference of 8 and 𝑎𝑛 = 154.
6. Find the first three terms of the arithmetic series
with 32 terms, a sum of 224 and 𝑎𝑛 = −86.
7. ∑16
𝑘=1(4𝑘 − 2)