IB Math AA Topic 1

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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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How do you find the nth term of an arithmetic sequence?

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The nth term (a_n) 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 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 nth term of a geometric sequence?

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The nth term (a_n) can be found 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 sigma notation?

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Sigma notation is a way to represent the sum of a sequence of numbers using the Greek letter sigma (Σ). It allows for concise expression of sums.

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How do you evaluate a geometric series?

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A geometric series can be evaluated using the formula: S_n = a_1 * (1 - r^n) / (1 - r), where S_n is the sum of the first n terms, a_1 is the first term, and r is the common ratio.

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What is the common ratio in a geometric sequence?

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The common ratio is the factor by which we multiply each term to get the next term in a geometric sequence.

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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.

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What is the formula for the sum of the first n terms of an arithmetic series?

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The sum S_n 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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What is an exponential equation?

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An exponential equation is an equation in which variables appear as exponents.