4.7: Arithmetic sequences
I can write a recursive formulas
given a sequence.
Day 1
Describe a pattern in each sequence. Then find the next two terms.
22 …
7, 10, 13, 16 ___,
19 ___,
Add 3
48 …
3, 6, 12, ___,
24 ___,
Mult by 2
66 ___,
99, 88, 77, ___,
55 …
Subtract 11
Arithmetic
sequences:
Ex:
In an arithmetic sequence: The
difference between each consecutive
term is constant. This difference is
called the common difference (d).
3, 5, 7, 9, …
Common difference for the above sequence:
2
If there is a common difference, what is it?
22 …
7, 10, 13, 16 ___,
19 ___,
48 …
3, 6, 12, ___,
24 ___,
Common difference:
3
Common difference:
There isn’t one.
66 ___,
99, 88, 77, ___,
55 …
Common difference:
-11
Is the following sequence arithmetic? If it is, describe the pattern.
a. 5, 10,
no
20, 40, …
Why not: I started with 5 and then
multiplied by 2 each time.
b. 5, 8, 11, 14…
yes
I started with 5 and then added 3
each time.
c. 20, 5, -10, -25, …
I started with 20 and then added
yes
-15 each time.
Recursive Formula:
An ordered list of numbers defined by a starting
value (number) and a rule to find the general
term.
A(1) = first term
A(n-1)= Previous term
A(n) = General term or nth term
Given the following recursive formula, find the first 4 terms.
A(1) = 20
20,
26, 32,
38
A(n) = A(n-1) + 6
Think: previous term + 6
1st term
2nd term
3rd term 4th term
Given the following recursive formula, find the first 4 terms.
A(1)=
-18
A(n) = A(n-1) - 3
Think: previous term -3
-18,
-21,
1st term
2nd term
-24,
-27,
3rd term 4th term
Write a recursive formula for each sequence.
7 10, 13, 16, …
7,
7
A(1) = ______
+3
A(n) = A(n-1)_____
A(1) = 7
A(n)
A(n-1)
+3
3
3, =9,15,
21,…
A(1) ==33
A(1)
A(n)
+ 6+ 6
A(n)= =A(n-1)
A(n-1)
(always has two parts)
Recursive rule:
A(1) = ____
A(n) = A(n-1) + d
97, 87, 77, 67 …
A(1) = 97
A(n) = A(n-1) - 10
Homework: pg 279: 9-35