Aim #87 : What is an arithmetic sequence?
Homework : Handout
Do Now : Write the recursive formula and find the next term for:
a. 2, 5, 8, 11, ... b. 8, 19, 30, 41, ...
A sequence is called arithmetic if there is a real number, d, such that each term in
the sequence is the sum of the previous term and d.
Arithmetic sequences are often called "linear sequences."
Write the recursive and explicit formula for the following sequences:
a) 4, 6, 8, 10, ... b) -2, -3, -4, -5, ...
Recursive: Recursive:
Explicit: Explicit:
To find a explicit formula for an arithmetic sequence:
a
n
= a
1
+ d(n - 1)
where a
n
is the value of the n
th
term, a
1
is the first term, and d is the common
difference. We then simplify to get the formula in the easiest form to work with.
The recursive formula is
a
n+1
= a
n
+ d
