This lesson covers geometric sequences as exponential functions. It explains how to identify and generate geometric sequences, relate them to exponential functions, and determine if a sequence is arithmetic, geometric, or neither. The lesson also includes methods to find the next terms in a sequence and introduces the formula for finding the nth term of a geometric sequence. Finally, it connects geometric sequences to exponential functions through real-world examples.

What is a geometric sequence?

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

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

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

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

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In a geometric sequence, what is the common ratio?

• The sum of consecutive terms.

• The product of consecutive terms.

• The difference between consecutive terms.

• The factor by which each term is multiplied to get the next term.

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How do you determine if a sequence is arithmetic?

• By checking if each term is squared.

• By checking if each term is divided by a common ratio.

• By checking if each term is added or subtracted by the same amount.

• By checking if each term is multiplied by a common ratio.

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What is the common difference in an arithmetic sequence?

• The product of consecutive terms.

• The difference between consecutive terms.

• The sum of consecutive terms.

• The ratio between consecutive terms.

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If a sequence is neither arithmetic nor geometric, what does it mean?

• The sequence has no pattern.

• The sequence is both arithmetic and geometric.

• The sequence has a changing common ratio or difference.

• The sequence is a constant value.

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

• By dividing the last term by the common ratio.

• By adding the common difference to the last term.

• By subtracting the common difference from the last term.

• By multiplying the last term by the common ratio.

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

• a_n = a_1 * r^(n-1)

• a_n = a_1 - (n-1)d

• a_n = a_1 + (n-1)d

• a_n = a_1 / r^(n-1)

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In the formula a_n = a_1 * r^(n-1), what does a_1 represent?

• The nth term of the sequence.

• The common ratio.

• The first term of the sequence.

• The number of terms in the sequence.

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What happens to the height of a tennis ball after each bounce if it bounces to 80% of its previous height?

• The height increases.

• The height remains the same.

• The height decreases by 80%.

• The height decreases by 20%.

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If a tennis ball is dropped from a height of 12 feet and bounces to 80% of its previous height, what is the height after the first bounce?

• 6.4 feet

• 4.8 feet

• 7.2 feet

• 9.6 feet

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