Arithmetic and 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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What is the common difference in an arithmetic sequence?

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

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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, d is the common difference, and n is the term number.

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

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What is the common ratio in a geometric sequence?

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

Tags

CCSS.HSF.BF.A.2

Front

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

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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, r is the common ratio, and n is the term number.

Tags

CCSS.HSF.BF.A.2

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What is the explicit formula for an arithmetic sequence?

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The explicit formula for an arithmetic sequence is a_n = a_1 + (n-1)d.

Tags

CCSS.HSF.BF.A.2

Front

What is the explicit formula for a geometric sequence?

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The explicit formula for a geometric sequence is a_n = a_1 * r^(n-1).

Tags

CCSS.HSF.BF.A.2

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How do you calculate 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 S_n is the sum, a_1 is the first term, and a_n is the nth term.

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How do you calculate 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), where S_n is the sum, a_1 is the first term, r is the common ratio, and n is the number of terms.

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CCSS.HSA.SSE.B.4