Arithmetic Sequences and Linear Functions Review

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Front

What is the explicit formula for an arithmetic sequence?

Back

The explicit formula is given by a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, n is the term number, and d is the common difference.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, defined by the equation f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope of a linear function from a graph?

Back

The slope (m) is calculated as the rise over run, which is the change in y divided by the change in x between two points on the line.

Front

What does the y-intercept represent in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of f(x) when x = 0.

Front

What is the relationship between arithmetic sequences and linear functions?

Back

Both arithmetic sequences and linear functions have a constant rate of change, meaning they increase or decrease by the same amount over equal intervals.

Front

How can you convert an explicit formula of an arithmetic sequence into function form?

Back

To convert to function form, express the nth term as a function of n, such as f(n) = a_1 + (n-1)d.

Front

What is the formula to find the nth term of a linear function?

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The nth term of a linear function can be found using the formula f(n) = mn + b, where m is the slope and b is the y-intercept.

Front

How do you determine the value of x when f(x) is given?

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To find x when f(x) = k, set the function equal to k and solve for x.

Front

What is the significance of a constant rate of change in a linear function?

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A constant rate of change indicates that the function is linear, meaning it will graph as a straight line.