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.

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CCSS.HSF.BF.A.2

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What is the common ratio in a geometric sequence?

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The common ratio (r) is the factor by which we multiply each term to get the next term in a geometric sequence.

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CCSS.HSF.BF.A.2

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How can you determine if a sequence is geometric?

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A sequence is geometric if the ratio of consecutive terms is constant.

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 (a_n) 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

Find the 5th term of the geometric sequence: 2, 6, 18, ...

Back

The 5th term is 162.

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 4, what is the 4th term?

Back

The 4th term is 192.

Tags

CCSS.HSF.BF.A.2

Front

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

Back

The sum (S_n) of the first n terms can be calculated using the formula: 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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Calculate the sum of the first 5 terms of the geometric sequence: 1, 2, 4, 8, ...

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The sum is 31.

Tags

CCSS.HSA.SSE.B.4

Front

Is the sequence 5, 10, 20, 40, ... geometric?

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Yes, it is geometric with a common ratio of 2.

Tags

CCSS.HSF.BF.A.2

Front

What is the 10th term of the geometric sequence: 1, 3, 9, 27, ...?

Back

The 10th term is 19,683.

Tags

CCSS.HSF.BF.A.2