Recursive and Geometric Sequences

This video tutorial explains how sequences can be understood as functions and how to use function notation to create recursive formulas. It covers arithmetic sequences, which have a constant difference and form linear functions, and geometric sequences, which have a common ratio and form exponential functions. The video also discusses the Fibonacci sequence, which is neither arithmetic nor geometric, and demonstrates how to write recursive formulas for each type of sequence using function notation.

What does the notation f(x) represent in function notation?

• The input value of x

• The output value when x is the input

• The difference between terms

• The ratio of terms

In an arithmetic sequence, what is the relationship between consecutive terms?

• They have a constant difference

• They are multiplied by a constant

• They are divided by a constant

• They have a common ratio

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

• Subtract a constant from the previous term

• Add a constant to the previous term

• Divide the previous term by a constant

• Multiply the previous term by a constant

What is the common ratio in the geometric sequence 3, 9, 27, 81?

• 2

• 3

• 4

• 5

In a geometric sequence, how is each term related to the previous one?

• By dividing by a constant

• By multiplying by a constant

• By subtracting a constant

• By adding a constant

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

How is the Fibonacci sequence different from arithmetic and geometric sequences?

• Each term is the sum of the two preceding terms

• Each term is the product of the two preceding terms

• It has a common ratio

• It has a constant difference

What is the recursive formula for the Fibonacci sequence?

• f(n) = f(n-1) + f(n-2)

• f(n) = f(n-1) * f(n-2)

• f(n) = f(n-1) / f(n-2)

• f(n) = f(n-1) - f(n-2)

In the Fibonacci sequence, what is the value of the third term if the first two terms are 1?

• 4

• 3

• 2

• 1

What is the main takeaway from learning about recursive formulas in sequences?

• They provide a way to express sequences using previous terms

• They are only applicable to arithmetic sequences

• They help in finding the sum of sequences

• They are only applicable to geometric sequences