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What is an arithmetic sequence?

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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?

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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.

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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, 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?

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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?

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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?

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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.