Arithmetic & Geometric Sequences

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What is an arithmetic sequence?

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An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

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CCSS.HSF.BF.A.2

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How do you find the nth term of an arithmetic sequence?

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The nth term of an arithmetic sequence can be found using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Tags

CCSS.HSF.BF.A.2

Front

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.

Tags

CCSS.HSF.BF.A.2

Front

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

Back

The nth term of a geometric sequence can be found 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

What is the common difference in an arithmetic sequence?

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

Tags

CCSS.HSF.BF.A.2

Front

What is the common ratio in a geometric sequence?

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The common ratio in a geometric sequence is the fixed number that each term is multiplied by to get the next term, denoted as r.

Tags

CCSS.HSF.BF.A.2

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How can you determine if a sequence is arithmetic?

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To determine if a sequence is arithmetic, check if the difference between consecutive terms is constant.

Tags

CCSS.HSF.BF.A.2

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How can you determine if a sequence is geometric?

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To determine if a sequence is geometric, check if the ratio of consecutive terms is constant.

Tags

CCSS.HSF.BF.A.2

Front

What is the formula for the sum of the first n terms of an arithmetic sequence?

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The sum of the first n terms of an arithmetic sequence can be calculated using the formula: S_n = n/2 * (a_1 + a_n), where a_n is the nth term.

Front

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

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The sum of the first n terms of a geometric sequence can be calculated using the formula: S_n = a_1 * (1 - r^n) / (1 - r) for r ≠ 1.

Tags

CCSS.HSA.SSE.B.4