Recursive Sequences

What is the common ratio in the sequence {7, 35, 175, 875, ...}?

• 2

• 3

• 4

• 5

How do you determine if a sequence is geometric?

• A sequence is geometric if each term after the first is found by adding a constant to the previous term.

• A sequence is geometric if each term after the first is found by multiplying the previous term by a constant called the common ratio.

• A sequence is geometric if the difference between consecutive terms is constant.

• A sequence is geometric if the ratio between consecutive terms is constant.

What is the first term in the sequence defined by a_n = 2a_(n-1) + n with a_0 = 0?

• 0

• 1

• 2

• 3

What is the recursive rule for the Fibonacci sequence?

• f_n = f_(n-1) + f_(n-2) with initial conditions f_0 = 0 and f_1 = 1.

• f_n = f_(n-1) - f_(n-2) with initial conditions f_0 = 1 and f_1 = 1.

• f_n = 2*f_(n-1) with initial conditions f_0 = 0 and f_1 = 1.

• f_n = f_(n-1) + 2*f_(n-2) with initial conditions f_0 = 0 and f_1 = 1.

What is the significance of the initial term in a recursive sequence?

• It determines the common difference in an arithmetic sequence.

• It serves as the starting point for generating all subsequent terms in the sequence.

• It is irrelevant to the sequence's behavior.

• It defines the maximum value of the sequence.

What is the first four terms of the sequence defined by a_n = 2a_(n-1) + n with a_0 = 0?

• 0, 1, 4, 10

• 0, 1, 4, 11

• 0, 2, 4, 11

• 1, 2, 3, 4

What is the recursive rule for the sequence {1, 2, 3, 5, 8, ...}?

• f_n = f_(n-1) + f_(n-2) with f_1 = 1 and f_2 = 2

• f_n = f_(n-1) + f_(n-2) with f_1 = 0 and f_2 = 1

• f_n = 2 * f_(n-1) with f_1 = 1

• f_n = f_(n-1) + 2 with f_1 = 1

What is the recursive rule for the sequence {16, 8, 4, 2, ...}?

• a_n = a_(n-1) * (1/2) with a_1 = 16

• a_n = a_(n-1) + 4 with a_1 = 16

• a_n = a_(n-1) - 2 with a_1 = 16

• a_n = a_(n-1) * 2 with a_1 = 16

How do you find the next term in a recursive sequence?

• Apply the recursive formula using the previous term(s) in the sequence.

• Add a constant value to the previous term.

• Multiply the previous term by a fixed number.

• Use the first term as the next term.

What is the general form of a recursive formula?

• a_n = f(a_(n-1), a_(n-2), ..., n)

• a_n = a_(n-1) + a_(n-2)

• a_n = n^2 + c

• a_n = a_0 + n * d