Arithmetic-Geometric series

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What is an Arithmetic-Geometric series?

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An Arithmetic-Geometric series is a series where each term is the product of an arithmetic sequence and a geometric sequence.

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Define the common ratio in a geometric series.

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The common ratio (r) in a geometric series is the factor by which each term is multiplied to obtain the next term.

Tags

CCSS.HSF.BF.A.2

Front

What is the formula for the sum of the first n terms of a geometric series?

Back

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CCSS.HSA.SSE.B.4

Front

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

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Tags

CCSS.HSF.BF.A.2

Front

What is the first term in the series 1, 5, 25, 125?

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The first term (a) is 1.

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CCSS.HSF.BF.A.2

Front

If the common ratio of a geometric series is 5, what is the second term if the first term is 1?

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The second term is 1 x 5 = 5.

Tags

CCSS.HSF.BF.A.2

Front

What happens to the sum of a geometric series if the common ratio is greater than 1?

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If the common ratio is greater than 1, the sum diverges to infinity as n approaches infinity.

Tags

CCSS.HSA.SSE.B.4

Front

Can the sum of a geometric series be negative?

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Yes, if the first term is negative and the common ratio is positive but less than 1, the sum can be negative.

Tags

CCSS.HSA.SSE.B.4

Front

What is the significance of the common ratio being less than 1 in a geometric series?

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If the common ratio is less than 1, the series converges, meaning the sum approaches a finite limit as n increases.

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What is the sum of the first 4 terms of the geometric series 1 + 0.5 + 0.25 + ?

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The sum is 1.875.

Tags

CCSS.HSA.SSE.B.4