Classwork #1

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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 found using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term, r is the common ratio, and n is the term number.

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What is the Box Method in algebra?

Back

The Box Method is a visual way to multiply polynomials by creating a box (or grid) to organize the terms. Each box represents the product of the terms from the two polynomials.

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How do you multiply two binomials?

Back

To multiply two binomials, use the distributive property (FOIL method): First, Outer, Inner, Last. For example, (a + b)(c + d) = ac + ad + bc + bd.

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What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other, using symbols like >, <, ≥, or ≤.

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What does it mean to solve a system of inequalities?

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Solving a system of inequalities involves finding all the values that satisfy all inequalities in the system simultaneously, often represented graphically.

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What is the square of a binomial?

Back

The square of a binomial (a + b)^2 is calculated as a^2 + 2ab + b^2.

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What is the common ratio in a geometric sequence?

Back

The common ratio is the factor by which each term in a geometric sequence is multiplied to get the next term. It is found by dividing any term by the previous term.

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How do you determine if a sequence is geometric?

Back

A sequence is geometric if the ratio between consecutive terms is constant. If a_n/a_(n-1) = r for all n, then the sequence is geometric.

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What is the significance of the first term in a geometric sequence?

Back

The first term (a_1) is the starting point of the sequence and is essential for calculating any other term using the formula a_n = a_1 * r^(n-1).

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What is the difference between a polynomial and a binomial?

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A polynomial is an expression with multiple terms, while a binomial is a specific type of polynomial that has exactly two terms.