Download Understanding Recursive and Explicit Formulas in Sequences and more Lecture notes Calculus in PDF only on Docsity! 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. Geometric Sequences: Recursive Steps: 1. Determine the first term ( ) and common ratio ( ) 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 ratio ( ) 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. Geometric Sequences: Recursive Steps: 3. Determine the first term ( ) and common ratio ( ) 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 ratio ( ) 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.
