Geometric Sequences

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What is a geometric sequence?

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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.

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CCSS.HSF.BF.A.2

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How do you determine if a sequence is geometric?

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A sequence is geometric if the ratio of any term to its preceding term is constant.

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CCSS.HSF.BF.A.2

Front

What is the common ratio in a geometric sequence?

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The common ratio is the factor by which we multiply each term to get the next term in the sequence.

Tags

CCSS.HSF.BF.A.2

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If the first term of a geometric sequence is 3 and the common ratio is 2, what are the first four terms?

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3, 6, 12, 24.

Tags

CCSS.HSF.BF.A.2

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What is the explicit formula for a geometric sequence?

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The explicit formula is a_n = a_1 * r^(n-1), where a_1 is the first term, r is the common ratio, and n is the term number.

Tags

CCSS.HSF.BF.A.2

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What is the 5th term of the geometric sequence 2, 6, 18, 54...?

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The 5th term is 162.

Tags

CCSS.HSF.BF.A.2

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How do you find the nth term of a geometric sequence?

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Use the formula a_n = a_1 * r^(n-1), substituting the values for a_1 and r.

Tags

CCSS.HSF.BF.A.2

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

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The sum S_n = a_1 * (1 - r^n) / (1 - r) for r ≠ 1.

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CCSS.HSA.SSE.B.4

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If a geometric sequence has a common ratio of 1/2 and the first term is 8, what is the 4th term?

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The 4th term is 1.

Tags

CCSS.HSF.BF.A.2

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What is the relationship between geometric sequences and exponential functions?

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Geometric sequences can be represented by exponential functions, as each term can be expressed as a constant multiplied by a power of the common ratio.