Arithmetic and Geometric Series

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What is an arithmetic series?

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An arithmetic series is the sum of the terms in an arithmetic sequence, where each term is obtained by adding a constant difference to the previous term.

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What is a geometric series?

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A geometric series is the sum of the terms in a geometric sequence, where each term is obtained by multiplying the previous term by a constant ratio.

Tags

CCSS.HSA.SSE.B.4

Front

How do you find the sum of the first n terms of an arithmetic series?

Back

The sum S_n of the first n terms of an arithmetic series can be calculated using the formula: S_n = n/2 * (a + l), where a is the first term and l is the last term.

Front

How do you find the sum of the first n terms of a geometric series?

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The sum S_n of the first n terms of a geometric series can be calculated using the formula: S_n = a * (1 - r^n) / (1 - r), where a is the first term and r is the common ratio.

Tags

CCSS.HSA.SSE.B.4

Front

Evaluate the geometric series: 1 - 2 + 4 - 8 + ... (n=8)

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The sum is -85.

Tags

CCSS.HSA.SSE.B.4

Front

Evaluate the arithmetic series: 2 + (-2) + (-6) + (-10)..., S_10

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The sum S_10 is -160.

Front

What is the common difference in an arithmetic sequence?

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The common difference is the constant amount that each term increases or decreases by in an arithmetic sequence.

Tags

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 is the constant factor by which each term in a geometric sequence is multiplied to get the next term.

Tags

CCSS.HSF.BF.A.2

Front

Evaluate S_8: 2 + 6 + 10 + 14 + ...

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The sum S_8 is 128.

Front

True or False: An arithmetic series is the sum of the terms in an arithmetic sequence.

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True.