9th Grade Final Exam

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What is a recursive formula?

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A recursive formula defines the terms of a sequence using previous terms. For example, a(n) = a(n - 1) - 2 defines each term based on the one before it.

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What is the definition of a function?

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A function is a relation where each input has exactly one output. If an input corresponds to multiple outputs, it is not a function.

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What is an explicit formula?

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An explicit formula provides a direct way to calculate the nth term of a sequence without needing to know previous terms. For example, y = 2 + 6x.

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How do you solve a system of linear equations?

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You can solve a system of linear equations using methods such as substitution, elimination, or graphing to find the values of the variables that satisfy both equations.

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What is a common difference in an arithmetic sequence?

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The common difference is the constant amount that each term in an arithmetic sequence increases or decreases by. For example, in the sequence -34, -29, -24, -19, the common difference is 5.

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What is the first term in the sequence defined by a(0) = 6?

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The first term is 6, as defined by the recursive formula.

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What does it mean for a sequence to be arithmetic?

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

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How can you identify if a relation is a function from a table?

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To determine if a relation is a function from a table, check if any input (x-value) is associated with more than one output (y-value). If it is, it is not a function.

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What is the formula for the nth term of the sequence 2, 8, 14, ...?

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The explicit formula is y = 2 + 6x, where x is the term number starting from 0.

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What is the solution to the system of equations 5x - 3y = -36 and 2x + 3y = 15?

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The solution is (-3, 7).