Arithmetic and Geometric Sequences Recursive and Explicit Formulas Flashcards
Arithmetic and Geometric Sequences Recursive and Explicit Formulas
What is a(1)?
the first term in the sequence
What is (a)n?
the nth term
What is a(n-1)?
the term BEFORE the nth term
What is d?
the common difference (could be negative)
What is r?
common ratio (could be fraction)
What is an explicit formula?
You are able to find the nth term without knowing the previous term
What is a recursive formula?
must know previous term
What is the Recursive Formula for an Arithmetic Sequence?
a(n)=a(n-1)+d
a1= 1st term
What is the Recursive Formula for a Geometric Sequence?
f(n)=f(n-1)r
f1= 1st term
What is the Explicit Formula for an Arithmetic Sequence.
fn = f(1)+d(n-1)
What is the Explicit Formula for a Geometric Sequence?
a1(r) to the power of n-1
Or
a0(r)of n
When writing the formula what are the only 3 things you fill in?
a1, d, r
What is an Arithmetic Sequence?
an expression with a common difference
(+ or -)
What is a Geometric Sequence?
where the next term is found by multiplying the term by the common ratio
(x)
What is a Quadratic Sequence?
2nd differences
