Arithmetic 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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What is the common difference in an arithmetic sequence?

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The common difference is the constant amount that is added to each term to get the next term in the sequence.

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How do you find the explicit formula for an arithmetic sequence?

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The explicit formula for 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.

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What is the recursive formula for an arithmetic sequence?

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

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Given the sequence 8, 11, 14, 17, 20, what is the first term (a_1)?

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The first term (a_1) of the sequence is 8.

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For the sequence 8, 11, 14, 17, 20, what is the 6th term (a_6)?

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The 6th term (a_6) of the sequence is 23.

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What is the value of a_0 in the sequence 8, 11, 14, 17, 20?

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The value of a_0 in the sequence is 5.

Front

How can you determine the nth term of an arithmetic sequence?

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You can determine the nth term of an arithmetic sequence using the explicit formula: a_n = a_1 + (n - 1)d.

Front

What is the significance of the first term in an arithmetic sequence?

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The first term is the starting point of the sequence and is essential for calculating other terms using the explicit formula.

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If the common difference is negative, what type of sequence is it?

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If the common difference is negative, the sequence is decreasing.