Arithmetic Sequence

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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.

Tags

CCSS.HSF.BF.A.2

Front

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 the common difference in an arithmetic sequence?

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The common difference is the constant amount that each term in the sequence increases or decreases by, calculated as d = a_(n+1) - a_n.

Tags

CCSS.HSF.BF.A.2

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If the first term of an arithmetic sequence is 5 and the common difference is 2, what is the 10th term?

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The 10th term can be calculated as a_10 = 5 + (10-1) * 2 = 5 + 18 = 23.

Tags

CCSS.HSF.BF.A.2

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What does a_1 represent in an arithmetic sequence?

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a_1 represents the first term of the arithmetic sequence.

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

Front

What is the explicit formula for the nth term of an arithmetic sequence?

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

Tags

CCSS.HSF.BF.A.2

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Given the sequence 3, 7, 11, 15, what is the common difference?

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The common difference is 4, calculated as 7 - 3 = 4.

Tags

CCSS.HSF.BF.A.2

Front

What is the 63rd term of the arithmetic sequence -1, 5, 11, ...?

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The 63rd term is 371, calculated using the formula a_n = a_1 + (n-1)d.

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 formula for the sum of the first n terms (S_n) of an arithmetic sequence is S_n = n/2 * (a_1 + a_n).