Download Sequences - Finding a rule

How to find a rule
• 1) Look for a common difference.
This is your Coefficient.
• 2) Go back to your first term and
subtract the common difference.
This is your constant.
For example: 1, 3, 5, 7, …
(This is a sequence of odd numbers)
1st term = = 1
2nd term = = 3
3rd term = = 5
.
.
.
nth term =
.
.
.
2xn–1
+2
+2
Common differencefirst term = constant.
= 2n - 1
NOTATION
1st term =
2nd term =
3rd term =
.
.
.
t1
t2
t3
.
.
.
nth term =
tn
Rank(n)
Term
1st term
t1
2nd term
t2
3rd term
t3
4th term
t4
Nth term
tn
Constant difference: coefficient of n is the difference
2
2nd
level difference: compare with square numbers
(n
= 1, 4, 9, 16, …)
3
3rd level difference: compare with cube numbers
(n
= 1, 8, 27, 64, …)
EXAMPLE:
Find the next three terms in the sequence 5, 8, 11, 14, …
Find the rule:
Rank(n)
Term
1
5
2
8
3
11
4
14
5
…..
6
7
EXAMPLE:
Find the nth term of the sequence 5,10,15,20,25
Find the rule:
Rank(n)
Term
1
5
2
10
3
15
4
20
5
6
7
Example
• Find the rule for the following:
Rank(n)
Term
1
2
2
4
3
9
4
16
5
6
7
n
Example:
• Find the 100th term in this sequence
if the rule is t=5r-10
Example:
• Ms. Mandigo joins a walking group.
The first day I walk 1km.I have to
increase my walking 0.5 km per day.
• How much will I walk on the 5th day?
Rank
Days
1
Term
1km
2
3
4
5
Example
• What's the rule for the pervious
example?
• Which day will I walk 19km?