1st Sem Alg 2 Final Exam Fall 2024

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What is the formula for the nth term of a geometric sequence?

Back

The nth term of a geometric sequence can be expressed as A(n) = a * r^(n-1), where 'a' is the first term and 'r' is the common ratio.

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How do you find the 5th term of the sequence A(n) = 3 * 2^(n-1)?

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To find A(5), substitute n=5 into the formula: A(5) = 3 * 2^(5-1) = 3 * 16 = 48.

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What are x-intercepts in a polynomial function?

Back

X-intercepts are the points where the graph of the polynomial crosses the x-axis, meaning the value of y is zero.

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How do you determine the polynomial with given x-intercepts?

Back

To find the polynomial, use the x-intercepts to form factors: If x-intercepts are x=a, x=b, and x=c, the polynomial can be expressed as y = k(x-a)(x-b)(x-c), where k is a constant.

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What is the difference between an arithmetic sequence and a geometric sequence?

Back

An arithmetic sequence has a common difference (rate of change), while a geometric sequence has a common ratio (growth factor).

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Back

Front

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

Back

The nth term of an arithmetic sequence can be expressed as A(n) = a + (n-1)d, where 'a' is the first term and 'd' is the common difference.

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

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What does it mean to simplify an expression?

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To simplify an expression means to reduce it to its simplest form, making it easier to understand or solve.

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What is the significance of the leading coefficient in a polynomial?

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The leading coefficient is the coefficient of the term with the highest degree in a polynomial, and it affects the end behavior of the polynomial's graph.