arithmetic sequence

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is an ordered set of numbers in which the difference between consecutive terms is constant.

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the fixed amount added to each term to get the next term in the sequence.

Front

If the first term of an arithmetic sequence is 5 and the common difference is 3, what is the second term?

Back

The second term is 8.

Front

If the first term of an arithmetic sequence is 10 and the common difference is -2, what is the fifth term?

Back

The fifth term is 2.

Front

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

Back

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

Front

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

Back

The sum S_n of the first n terms is given by S_n = n/2 * (a_1 + a_n), where a_n is the nth term.

Front

What is the difference between a function and a non-function?

Back

A function assigns exactly one output for each input, while a non-function may assign multiple outputs for a single input.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function; if a vertical line intersects the graph at more than one point, it is not a function.

Front

Given the function f(x) = 2x + 3, find f(2).

Back

f(2) = 7.

Front

Given the function f(x) = -x^2 + 4, find f(0).

Back

f(0) = 4.