Algebra - Topic 3 Review - Part 2

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What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. For example, 2, 4, 6, 8 is an arithmetic sequence with a common difference of 2.

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

Back

The nth term of an arithmetic sequence can be found using the formula: a_n = a_1 + (n - 1)d, where a_1 is the first term, d is the common difference, and n is the term number.

Front

What is a recursive formula?

Back

A recursive formula defines the terms of a sequence using previous terms. For example, in the sequence of even numbers, a_n = a_{n-1} + 2, with a_1 = 2.

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What does the y-intercept of a line represent in a graph?

Back

The y-intercept is the point where the line crosses the y-axis. It represents the value of y when x = 0.

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What is correlation in data analysis?

Back

Correlation measures the relationship between two variables. It can be positive (both variables increase), negative (one variable increases while the other decreases), or zero (no relationship).

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

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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 the difference between a positive and negative correlation?

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A positive correlation means that as one variable increases, the other also increases. A negative correlation means that as one variable increases, the other decreases.

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How can you determine if a sequence is arithmetic?

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To determine if a sequence is arithmetic, check if the difference between consecutive terms is constant.

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What is the first term in the recursive formula a_n = a_{n-1} + 4, a_1 = 15?

Back

The first term a_1 is 15.

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What does it mean if a data set has no correlation?

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If a data set has no correlation, it means there is no discernible relationship between the two variables being analyzed.