Exploring Geometric Sequences and Their Formulas

What is a geometric sequence?

• A sequence where each term is divided by a common divisor.

• A sequence where each term is multiplied by a common ratio.

• A sequence where each term is added by a common difference.

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

How do you find the common ratio in a geometric sequence?

• By adding consecutive terms.

• By dividing any term by its preceding term.

• By subtracting any term from its preceding term.

• By multiplying any term with its preceding term.

What happens to the terms in a geometric sequence with a negative common ratio?

• They remain constant.

• They alternate between positive and negative.

• They all become negative.

• They all become positive.

What is the formula for the nth term of a geometric sequence?

• a_n = a_1 + r^(n-1)

• a_n = a_1 / r^(n-1)

• a_n = a_1 - r^(n-1)

• a_n = a_1 * r^(n-1)

If the first term of a geometric sequence is 5 and the common ratio is 3, what is the 3rd term?

• 15

• 45

• 405

• 135

What does the term 'a sub 1' refer to in the context of geometric sequences?

• The last term of the sequence.

• The first term of the sequence.

• The difference between terms.

• The common ratio.

How can the nth term formula for geometric sequences be used?

• To calculate the difference between terms.

• To find any specific term in the sequence.

• To determine the common ratio.

• To find the sum of all terms.

What is the 5th term of a geometric sequence where the first term is 2 and the common ratio is 3?

• 729

• 486

• 243

• 162

In a geometric sequence, if the common ratio is 1/2, what happens to the terms as the sequence progresses?

• They remain the same.

• They decrease.

• They increase.

• They become zero.

If a geometric sequence has a common ratio of -2, what is the 4th term given the first term is 1?

• -8

• -2

• 8

• 2