Geometric Sequences

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What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Tags

CCSS.HSF.BF.A.2

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

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The common ratio (r) can be found by dividing any term in the sequence by the previous term (r = a_n / a_(n-1)).

Tags

CCSS.HSF.BF.A.2

Front

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

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The nth term of a geometric sequence can be calculated using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Tags

CCSS.HSF.BF.A.2

Front

If the first term of a geometric sequence is 3 and the common ratio is 2, what is the 5th term?

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The 5th term is a_5 = 3 * 2^(5-1) = 3 * 16 = 48.

Tags

CCSS.HSF.BF.A.2

Front

What does the term 'common ratio' refer to in a geometric sequence?

Back

The common ratio is the constant factor between consecutive terms in a geometric sequence.

Tags

CCSS.HSF.BF.A.2

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Can a geometric sequence have a common ratio of zero?

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No, a geometric sequence cannot have a common ratio of zero, as this would not allow for a valid sequence of terms.

Tags

CCSS.HSF.BF.A.2

Front

What is the difference between an arithmetic sequence and a geometric sequence?

Back

An arithmetic sequence adds a constant value (common difference) to each term, while a geometric sequence multiplies each term by a constant value (common ratio).

Tags

CCSS.HSF.BF.A.2

Front

If a geometric sequence has a common ratio of -1/4, what is the second term if the first term is 64?

Back

The second term is 64 * (-1/4) = -16.

Tags

CCSS.HSF.BF.A.2

Front

What is the sum of the first n terms of a geometric sequence?

Back

The sum of the first n terms (S_n) of a geometric sequence can be calculated using the formula: S_n = a_1 * (1 - r^n) / (1 - r) for r ≠ 1.

Tags

CCSS.HSA.SSE.B.4

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What happens to the terms of a geometric sequence if the common ratio is greater than 1?

Back

If the common ratio is greater than 1, the terms of the geometric sequence will increase without bound.

Tags

CCSS.HSF.BF.A.2