Sequence and Series Worksheet #1 Date:______ 1) A table is

Advanced Algebra II
Sequence and Series Worksheet #1
Name:_________________________Per:______
Date:__________
1) A table is very useful when analyzing a sequence to determine its pattern. Consider the sequence
7, 10, 13, 16, … in the table below:
n 1 2 3 4 5 6 7
7 10 13 16
a) Fill in the rest of the table.
b) Graph this sequence. c) What does the graph look like?
d) What is the generator for the sequence?
a) This type of sequence is called an arithmetic sequence. The
generator in an arithmetic sequence is frequently called the
common difference. Why might this term be used?
f) How is the common difference related to the graph?
g) Use the graph to find the y-intercept?
h) How can calculate the y-intercept of the sequence without having
to graph it first? Do it.
i) What is the algebraic expression that will determine any term in the sequence?
j) Find
2) In the sequence 7, 10, 13, 16, … is it possible for 200 to be a value in the row? Explain your thinking.
3) Using what you learned from problem 1, find .
a) 5, 8, 11, 14, … b) 26, 21, 16, … c) 7, 8.5, 10, …

4) Consider the sequence 3, 6, 12, 24, …
a) Complete the table for the sequence.
n 1 2 3 4 5 6 7
3 6 12 24
b) What is the generator for this sequence?
c) How many times do you need to multiply the first term in the sequence of 3 by 2 in order to obtain the
value 24 in the sequence?
d) Is there a short cut for doing repeated multiplication? What is it?
e) The value found when n = 6 can be obtained by multiplying 3(2)(2)(2)(2)(2). Rewrite this expression
using exponents.
f) What will the representation be for the 100 th term of the sequence?
g) How could you represent ?
5) Using what you learned from problem 4, find for each sequence below.
a) 2, 8, 32, … b) 7, 42, 252, 1512, … c) 3072, 384, 48, 6, …
6) For each of the following sequences, state whether each is arithmetic or geometric. If arithmetic or
geometric, write the next 3 terms find and find .
a) 4, 9, 14, 19, … b) 24, 12, 6, 3, …. c) 91, 82, 73, 64, …..
d) 1, 4, 9, 16, ….. e) -9.5, -7, -4.5, -2, … f) -4, 8, -16, 32, ….

7) For each of the following sequences, determine if 335 is a term in the sequence.
a) = 5n – 30 b) = 6(n – 2) + 78
c) = -15n + 40 d) 3, 7, 11, 15, ….
8) An arithmetic sequence contains the following: = 46 and = 25. Find the equation for the sequence
algebraically and then determine .
9) Use the pattern below to determine how many tiles the 46 th figure of the sequence would have.
Figure 1 Figure 2 Figure 3 Figure 4
10) Factor Completely
a) 60 110 100 b) 64 27 5 45

11) Use the following functions to answer each of the following.
f(x) = 4 - (8x – 6) g(x) = 3x² - 5x h(x) =
2
x − 5
a) Find g(2). b) Find h(-3). c) Find x if g(x) = 12.
d) Find x if h(x) = 3. e) Find x if g(x) = 2. f) Find x if g(x) = 0.
12) Investigate each function below.
a) 8
b) 3 √4