A2A | U1Q2 | Sequences & Series (ATA Unit Test)

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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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What is a geometric sequence?

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A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

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

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The common difference (d) can be found by subtracting any term from the subsequent term: d = a_{n} - a_{n-1}.

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How do you find the common ratio in a geometric sequence?

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The common ratio (r) can be found by dividing any term by the previous term: r = a_{n} / a_{n-1}.

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What is the formula for the nth term of an arithmetic sequence?

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The nth term (a_n) of an arithmetic sequence can be calculated 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 a geometric sequence?

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The nth term (a_n) of a geometric sequence can be calculated using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

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What is the sum of the first n terms of an arithmetic sequence?

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The sum (S_n) of the first n terms of an arithmetic sequence 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 n terms of a geometric sequence?

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The sum (S_n) of the first n terms of a geometric sequence can be calculated using the formula: S_n = a_1 * (1 - r^n) / (1 - r), for r ≠ 1.

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What does it mean if a sequence is classified as 'neither' arithmetic nor geometric?

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A sequence is classified as 'neither' if it does not have a constant difference (arithmetic) or a constant ratio (geometric) between its terms.

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Given the sequence {600, -300, 100, -25,...}, classify it and explain why.

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The sequence is classified as 'neither' because it does not have a constant difference or a constant ratio between its terms.