Arithmetic Sequence

Front

What is an arithmetic sequence?

Back

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

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How do 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 the same.

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.

Front

Given the arithmetic sequence 2, 5, 8, 11, what is the common difference?

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The common difference is 3.

Front

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

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The nth term 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.

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What is the formula for the nth term of the arithmetic sequence 4, 8, 12?

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The formula is a_n = 4 + (n-1)4.

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What is the 10th term of the arithmetic sequence 7, 10, 13, ...?

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The 10th term is 34.

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

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

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What is the sum of the first 5 terms of the arithmetic sequence 1, 3, 5, 7, 9?

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The sum is 25.

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What is a recursive formula for an arithmetic sequence?

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A recursive formula expresses each term based on the previous term, e.g., a_n = a_(n-1) + d.