Difference Between Recursive and Explicit Formulas
Recursive: A formula for the next term, depending on the previous term
Explicit: A formula for any term, depending on the term number
Arithmetic Sequences:
Recursive
Steps:
1. Determine the first term ( ) and common
difference ( )
2. Substitute into:
And state the first term
What it’s used for: Describing the pattern and finding
the next few terms
Example:
Write the recursive formula for the following
sequence:
1. and
2.
Step 2 is the entire recursive formula. You must have
both parts.
Explicit
Steps:
1. Determine the first term ( ) and common
difference ( )
2. Substitute into:
What it’s used for: Finding any term as long as you
know the term number ( )
Example:
Write the explicit formula for the following sequence:
1. and
2.
Step 2 is the explicit formula.
If you know the term number, you can substitute that
for to determine the term value.
Difference Between Recursive and Explicit Formulas
Recursive: A formula for the next term, depending on the previous term
Explicit: A formula for any term, depending on the term number
Arithmetic Sequences:
Recursive
Steps:
3. Determine the first term ( ) and common
difference ( )
4. Substitute into:
And state the first term
What it’s used for: Describing the pattern and finding
the next few terms
Example:
Write the recursive formula for the following
sequence:
3. and
4.
Step 2 is the entire recursive formula. You must have
both parts.
Explicit
Steps:
3. Determine the first term ( ) and common
difference ( )
4. Substitute into:
What it’s used for: Finding any term as long as you
know the term number ( )
Example:
Write the explicit formula for the following sequence:
3. and
4.
Step 2 is the explicit formula.
If you know the term number, you can substitute that
for to determine the term value.
