4.7: Arithmetic sequences

1
4.7 Arithmetic sequences

• I can write a recursive formulas given a sequence.

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