Name: __________________________________
Date: ______________________
Lesson 1 – Intro to Module 3
Think about it--What is the next number in the sequence
2, 4, 6, 8, …?
Other ideas:
Arithmetic Sequences
A sequence is an ordered list of
numbers. Each number of a sequence is
called a term (or element) of the sequence.
An arithmetic sequence follows a pattern
of adding a fixed amount from one term
to the next.
An explicit formula describes the nth term
of a sequence using the number n.
For example, if you wanted to know the 88th
term, just substitute 88 for 𝑛 and evaluate.
Example:
1. A sequence has an explicit formula 𝑎𝑛 =
3𝑛 − 2.
What are the first 5 terms of the sequence?
What is the common difference between
terms?
A recursive formula states the first term of
the sequence and relates subsequent terms
to the one before.
For example, if you wanted to know the 88th
term, you must know the 87th term to find it.
Example:
2. State the first 4 terms of the sequence:
𝑎1 = 12
𝑎𝑛 = 𝑎𝑛−1 + 5
What is the common difference?
3. Is the sequence 1, 4, 9, 16, 25 and
arithmetic sequence? Justify your
reasoning.
4. What is the 100th term of the arithmetic
sequence 6, 11, 16, … ?
5. What is the explicit formula for the nth
term of the sequence 1, 3, 5, 7, … ?
6. Write a recursive formula for the
sequence
1, 3, 5, 7, …
Check: For a and b: Which type of formula is
this? How do you know?
a.) 𝐴(𝑛+1)=𝐴(𝑛)+15
7. What is the missing term of the
arithmetic sequence …-7 , 15, ___ , 59, … ?
b.) 𝐴(𝑛) = 15 – 3(𝑛−1)
Name _______________________________
Sequences
Arithmetic
Show all your work
1. What is a formula for the nth term of sequence B shown below?
1)
2)
3)
4)
2. What is the common difference of the arithmetic sequence 5, 8, 11, 14?
3. Which arithmetic sequence has a common difference of 4?
1) 4, 16, 64, 256
2) 8, 4, 0, –4
3) 6, 10, 14, 18
4) 4, 8, 14, 18
4. Find the first four terms of the recursive sequence defined below.
5. Find the third term in the recursive sequence 𝑎𝑛 = 𝑎𝑛−1 − 1, where 𝑎1 = 3.
6. What are the first five terms of the sequence 𝑎𝑛 = 4𝑛 − 7.
What is the common difference?
7. State the first four terms of the sequence:
𝑎1 = 23
𝑎𝑛 = 𝑎𝑛−1 − 9
What is the common difference?
8. What is the 50th term of the arithmetic sequence 8, 14, 20, … ?
9. What is the explicit formula for the nth term of the sequence 10, 12.5, 15, 17.5 … ?
10. Write a recursive formula for the sequence 10, 8, 6, 4, …
11. What is the missing term of the arithmetic sequence …-19, 18, _____ , 92, … ?
Name: ___________________________________
Date: _________________
Ticket out the door
Lesson 1
Consider the sequence given by a “plus 8” pattern: 2,10,18,26, ….
Shae says that the formula for the sequence is an=8𝑛+2.
Marcus tells Shae that she is wrong because the formula for the
sequence is an =8𝑛−6.
a. Which formula generates the sequence by starting at 𝑛=1? At 𝑛=0?
b. Find the 100th term in the sequence.
Name: ___________________________________
Date: _________________
Ticket out the door
Lesson 1
Consider the sequence given by a “plus 8” pattern: 2,10,18,26, ….
Shae says that the formula for the sequence is an=8𝑛+2.
Marcus tells Shae that she is wrong because the formula for the
sequence is an =8𝑛−6.
a. Which formula generates the sequence by starting at 𝑛=1? At 𝑛=0?
b. Find the 100th term in the sequence.
****Teacher’s notes – optional problems
Problem set:
1. Consider a sequence generated by the
formula f(𝑛)= 6𝑛−4 starting with 𝑛=1.
Generate the terms f(1),f(2),𝑓(3),𝑓(4), and
𝑓(5).
In problems 2-5, for each of the following sequences:
a. Write a formula for the 𝑛th term of the sequence. Be sure to specify what value of 𝑛
your formula starts with.
b. Using the formula, find the 15th term of the sequence.
2. The sequence follows a “plus 2” pattern:
3,5,7,9, ….
a. Write a formula
b. Using the formula, find the 15th term
3. The sequence follows a “times 4” pattern:
1,4,16,64, ….
a. Write a formula
b. Using the formula, find the 15th term
4. The sequence follows a “times -1”
pattern: 6,–6,6,–6, ….
a. Write a formula
b. Using the formula, find the 15th term
5. The sequence follows a “minus 3”
pattern: 12,9,6,3, ….
a. Write a formula
b. Using the formula, find the 15th term