Unit 9 Test Review

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What is a recursive sequence?

Back

A recursive sequence is a sequence of numbers where each term is defined as a function of the preceding terms. For example, in the sequence defined by a_n = -3 + a_(n-1), each term is generated from the previous term.

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How do you find the first four terms of a recursive sequence?

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To find the first four terms of a recursive sequence, start with the initial term (a_1) and use the recursive formula to calculate each subsequent term. For example, if a_1 = 5 and a_n = -3 + a_(n-1), the first four terms are 5, 2, -1, -4.

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What is the square root of 75 simplified?

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The square root of 75 can be simplified to 5√3, since 75 = 25 * 3 and √25 = 5.

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What is a linear function?

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A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

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How do you interpret a scatterplot in relation to a linear function?

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A scatterplot shows the relationship between two variables. If the points form a pattern that resembles a straight line, a linear function can be used to model the relationship.

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What does the slope of a linear function represent?

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The slope of a linear function represents the rate of change of the dependent variable (y) with respect to the independent variable (x). A negative slope indicates a decrease in y as x increases.

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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 of a geometric sequence 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 the common ratio in a geometric sequence?

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The common ratio in a geometric sequence is the factor by which each term is multiplied to get the next term. For example, in the sequence -4, -16, -64, the common ratio is 4.

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What is the difference between a recursive sequence and an explicit formula?

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A recursive sequence defines each term based on previous terms, while an explicit formula allows you to calculate any term directly without needing the previous terms.