March 25, 2014
Arithmetic Sequence: Recursive Formula
Algebra II
3/25/14
HW: P596 #7-11, 28-31, 33
Warm Up: Identify the pattern for each
1, 3, 5, 7,...
3, 7, 11, 15,...
-2, -4, -8, -16,...
March 25, 2014
Arithmetic Sequence: is a sequence of numbers where the
difference between terms is constant. In other words, you
add the same amount to get from term to term.
What is the common difference for each?
1, 2, 3, 4,...
-1, -3, -5, -7,...
7, 13, 19, 25,...
10, 50, 90, 130,...
Arithmetic Sequence: Recursive Formula
an = an-1 + d
n: the position of the term
an : The nth term
an-1: The term before the nth term
d: The common difference
March 25, 2014
5, 9, 13, 17,...
a 1=
a 2=
a 4=
-3, -7, -11, -15, ...
a 1=
a 3=
a 5=
-30, 40, 110, 180,...
a 2=
a 4=
a 6=
Identify the common difference and write the
recursive formula for each.
35, 32, 29, 26,...
2, 15, 28, 41,...
-12, 3, 18, 33,...
March 25, 2014
Given the common difference and a1, write the
recursive formula and the first 5 terms of the
sequence.
1. d=4, a1=2
2. d=-2, a1=-4
Given d and an, find an+1 and an-1
1. d=2, an=3
2. d=3, an=5
an+1=
an+1=
an-1=
an-1=
3. d=-1, an=15
4. d=6, an=52
an+1=
an+1=
an-1=
an-1=
March 25, 2014