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. 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 \( a_n \) is the nth term, \( a_1 \) is the first term, and \( d \) is the common difference.

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What is the common difference in the sequence 5, 8, 11, 14?

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The common difference is 3, calculated as \( 8 - 5 = 3 \).

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Find the 10th term of the arithmetic sequence: 3, 7, 11, 15, ...

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The 10th term is 39, calculated using the formula: \( a_{10} = 3 + (10-1) \cdot 4 = 39 \).

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Identify the common difference in the sequence: 12, 9, 6, 3, ...

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The common difference is -3, calculated as \( 9 - 12 = -3 \).

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Is the sequence 2, 4, 8, 10 arithmetic?

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No, the sequence is not arithmetic because the differences between terms are not constant (2, 4, 2).

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What is the 25th term of the arithmetic sequence: 2, 4, 6, 8?

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The 25th term is 50, calculated using the formula: \( a_{25} = 2 + (25-1) \cdot 2 = 50 \).

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Find the 26th term in the arithmetic sequence: 20, 26, 32, 38, ...

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The 26th term is 170, calculated using the formula: \( a_{26} = 20 + (26-1) \cdot 6 = 170 \).

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

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Find the 11th term of the arithmetic sequence: 4, -3, -10, -17, ...

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The 11th term is -66, calculated using the formula: \( a_{11} = 4 + (11-1)(-7) = -66 \).