Download Period ____ Introduction To Patterns

Name ___________________________________________________ Period ____ Introduction To Patterns
I. Vocabulary
A. Sequence – A set of numbers in a specific order.
19, 21, 23, 25, 27, 29. …
B. Term – Each number in the sequence is called a term. We refer to the terms as the first term, the second
term, the third term……the tenth term….the seventeenth term.
0, 1, 4, 9, 16, 25, 36, ………
1. Zero is the ______________ term in the sequence
2. What number is the 4th term in the sequence? __________
C. Consecutive Terms - Terms that are right next to each other.
10, 20, 30, 40, 50, 60, 70, 80, 90, ……
1. In the sequence above, name three consecutive terms if you start with 40: _____________________
2. In the sequence above, are 20 and 40 consecutive terms? ________ Explain why: ______________
________________________________________________________________________________
D. Rule – A description of what you do to find each term in the sequence.
 A rule always begins with the words, “Start with…..” and then tells what to do to get the next
consecutive term.
 Caution: Most sequences usually have many rules that could work. It is best to say a rule rather
than the rule.
1. Write the first four terms in the sequences described by each rule below:
a. Start with 10, multiply by 3. __________, __________, __________, __________
b. Start with 1,multiply by 2 and add 1.
__________, __________, __________, __________
c. Start with 75, subtract 4. __________, __________, __________, __________
d. Start with 2, alternate between adding 3 and multiplying by 4. ______, ______, ______, ______
2. Examine each sequence, and write a rule to describe it. Then use the rule to write the next 2 terms.
a. 19, 21, 23, 25, 27, 29, __________, __________ RULE: _______________________________
b. 90, 80, 70, 60, 50, __________, __________
RULE: _______________________________
c. 12, 24, 48, 96, __________, __________
RULE: _______________________________
d. 0, 1, 4, 9, 16, 25, 36, __________, __________ RULE: _______________________________
E. Formula – A specific “recipe” that will allow you to find any term in the sequence without having to
find all of the previous terms.
 A formula uses the variable n to represent the position of any term (1st, 2nd, 3rd, 4th, etc.)
A. Consider the sequence: 3, 5, 7, 9…..

A rule could be, Start with 3, add 2.

What if I wanted to know the 100th term? It would take a lot of work to get there if I only use a
rule.

A formula would be so much more helpful! It can be tricky to write a formula. Let’s try:
1) Put your sequence into a table.
position of term (n)
1
2
3
4
term
3
5
7
9
5
6
7
2) Observe the relationship between n and the term.
3) Try a rule – you might not get it the first time!
 Does n +2 work? For the 1st term, but that is it.
 Does 3n work?
 Try something else. Notice the term is almost twice as big as n.
 What do you have to do to 2n to get the term? ___________
 Will it work every time? _______
 What is the formula for this sequence? ___________________________

Now, use the formula to get the 100th term: __________________
II. Arithmetic Sequence- A sequence where each term is found by adding or subtracting the same value from
one term to the next. We call this value the "common sum" or "common difference"
A) 1, 4, 7, 10, 13, 16, . . . is an arithmetic sequence since the common sum between consecutive terms is
always 3 (you are always adding 3 to get the next term).
B) 8, 6, 4, 2, 0, -2, -4, . . . is an arithmetic sequence since the common difference between consecutive
terms is always 2 (you are always subtracting 2 to get the next term).
III. Geometric Sequence - A sequence where each term is found by multiplying or dividing by the same value
to go from one term to the next.
A) 5, 10, 20, 40, 80 ….. is a geometric sequence because I multiply each term by 2 to get the next term.
B) 500, 100, 20, 4, 0.8 ….is a geometric sequence because I divide each term by 5 to get the next term.