Arithmetic Sequences Practice

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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. This difference is called the common difference.

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How do you find the common difference in an arithmetic sequence?

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The common difference can be found by subtracting any term from the subsequent term in the sequence. For example, in the sequence 3, 7, 11, the common difference is 7 - 3 = 4.

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What is the recursive formula for an arithmetic sequence?

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The recursive formula for an arithmetic sequence can be expressed as: a_n = a_(n-1) + d, where d is the common difference.

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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 given by: a_n = a_1 + (n - 1)d, where a_1 is the first term and d is the common difference.

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Given the first term a_1 = 2 and common difference d = 3, what are the first four terms of the sequence?

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The first four terms are: 2, 5, 8, 11.

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If the first term of an arithmetic sequence is -4 and the common difference is 6, what is the 5th term?

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The 5th term can be calculated as: a_5 = -4 + (5 - 1) * 6 = -4 + 24 = 20.

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What is the formula to 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.

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How do you determine the number of terms in an arithmetic sequence?

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To determine the number of terms in an arithmetic sequence, you can use the formula: n = (last term - first term) / d + 1.

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What is 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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If the common difference is negative, what does that indicate about the sequence?

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If the common difference is negative, it indicates that the sequence is decreasing.