Understanding Geometric Sequences

The video tutorial explains geometric sequences, where each term is the previous term multiplied by a constant. It covers both explicit and recursive definitions, providing examples of geometric sequences and contrasting them with non-geometric sequences. The tutorial also demonstrates how to calculate terms in these sequences.

What is a geometric sequence?

• A sequence where each term is divided by a constant.

• A sequence where each term is added by a constant.

• A sequence where each term is subtracted by a constant.

• A sequence where each term is multiplied by a constant.

How can a geometric sequence be defined explicitly?

• By stating the first term and the common ratio.

• By stating the first term and the common difference.

• By stating the last term and the common ratio.

• By stating the last term and the common difference.

What is the recursive definition of a geometric sequence?

• Each term is the product of the previous term and a constant.

• Each term is the sum of the previous term and a constant.

• Each term is the difference of the previous term and a constant.

• Each term is the quotient of the previous term and a constant.

In the example given, what is the first term of the geometric sequence?

• 10

• 15

• 25

• 20

What is the common ratio in the given geometric sequence example?

• 1/2

• 1

• 1/3

• 1/4

Why is the sequence starting with 1, 2, 6, 24 not geometric?

• Because each term is divided by a different number.

• Because each term is added by a different number.

• Because each term is multiplied by a different number.

• Because each term is subtracted by a different number.

What pattern does the non-geometric sequence follow?

• Each term is the product of the previous term and a constant.

• Each term is the product of the previous term and an increasing integer.

• Each term is the sum of the previous term and a constant.

• Each term is the sum of the previous term and an increasing integer.

How is the non-geometric sequence defined explicitly?

• Using powers.

• Using factorials.

• Using the product of integers.

• Using the sum of integers.

What is the recursive definition of the non-geometric sequence?

• Each term is the sum of the previous term and a constant.

• Each term is the product of the previous term and a constant.

• Each term is the sum of the previous term and the term number.

• Each term is the product of the previous term and the term number.

What is the first term of the non-geometric sequence?

• 3

• 2

• 1

• 0