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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 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.

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What is the common difference in the sequence 3, 7, 11, 15?

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The common difference is 4, as each term increases by 4.

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If the first term of an arithmetic sequence is 5 and the common difference is 3, what is the 10th term?

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The 10th term is 32, calculated as \( 5 + (10-1) \times 3 = 32 \).

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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: \( S_n = \frac{n}{2} (a_1 + a_n) \) or \( S_n = \frac{n}{2} (2a_1 + (n-1)d) \).

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What is the formula for the sum of an arithmetic series?

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The formula for the sum of an arithmetic series is: \( S_n = \frac{n}{2} (a_1 + a_n) \), where \( S_n \) is the sum, \( n \) is the number of terms, \( a_1 \) is the first term, and \( a_n \) is the last term.

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What is the difference between an arithmetic sequence and a geometric sequence?

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An arithmetic sequence has a constant difference between terms, while a geometric sequence has a constant ratio between terms.

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If an arithmetic sequence has a first term of 10 and a common difference of -2, what are the first five terms?

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The first five terms are 10, 8, 6, 4, 2.

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What is the 5th term of the arithmetic sequence 2, 5, 8, ...?

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The 5th term is 14, calculated as \( 2 + (5-1) \times 3 = 14 \).

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How do you determine if a sequence is arithmetic?

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A sequence is arithmetic if the difference between consecutive terms is constant.