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

Front

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

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

Tags

CCSS.HSA.SSE.B.4

Front

What is the common difference in an arithmetic series?

Back

The common difference is the constant amount that is added to each term to get the next term in an arithmetic sequence.

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CCSS.HSF.BF.A.2

Front

What is the common ratio in a geometric series?

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

Tags

CCSS.HSF.BF.A.2

Front

Calculate the sum of the first 6 terms of the geometric series: -4/5, 8, -80, 800, ...

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CCSS.HSA.SSE.B.4

Front

Find the sum of the first 25 terms of the series: 6 + 14 + 22 + 30 + ...

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S_{25} = 2550.

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If Mike's starting salary is $35,000 and increases by $1,200 each year, what is his total salary after 10 years?

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Total salary = $404,000.

Tags

CCSS.HSF.BF.A.2

Front

Find the sum of the first 718 terms of the series: 2 + 4 + 6 + ... + 1436.

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S_{718} = 516,242.