Creating Recursive Formulas Using Function Notation

This lesson teaches how to create recursive formulas using function notation. It covers arithmetic and geometric sequences, explaining how to derive recursive formulas for each. The lesson also addresses common misunderstandings with function notation and inputs. Finally, it explores the Fibonacci sequence, demonstrating how to create a recursive formula for it.

What is the main difference between an arithmetic sequence and a geometric sequence?

• Arithmetic sequences are random, while geometric sequences follow a pattern.

• Arithmetic sequences have a constant ratio, while geometric sequences have a constant difference.

• Arithmetic sequences have a constant difference, while geometric sequences have a constant ratio.

• Arithmetic sequences are exponential, while geometric sequences are linear.

In function notation, what does f(n) represent?

• The sum of all terms up to n.

• The product of the first n terms.

• The value of the nth term in a sequence.

• The difference between the nth and (n-1)th terms.

How do you determine the next term in an arithmetic sequence?

• Divide the previous term by a constant ratio.

• Add a constant difference to the previous term.

• Multiply the previous term by a constant ratio.

• Subtract a constant difference from the previous term.

What is the recursive formula for a geometric sequence with a common ratio of 3?

• f(n) = f(n-1) * 3

• f(n) = f(n-1) / 3

• f(n) = f(n-1) + 3

• f(n) = f(n-1) - 3

In the Fibonacci sequence, how is each term calculated?

• By multiplying the previous two terms.

• By adding the previous two terms.

• By subtracting the previous two terms.

• By dividing the previous two terms.