Algebra Midterm Review

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

The common difference can be found by subtracting any term from the subsequent term. For example, in the sequence 2, 5, 8, the common difference is 5 - 2 = 3.

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 and $$d$$ is the common difference.

A recursive formula defines each term of a sequence using the preceding term(s). For example, in the sequence 2, 5, 8, the recursive formula is $$a_n = a_{n-1} + 3$$ .

To write an equation for a situation, identify the variables involved and their relationships. For example, if Jessica eats 5 cookies per day from a total of 54, the equation is $$y = -5x + 54$$ .

The first term of the sequence is 18.

Use the formula $$a_n = a_1 + (n - 1)d$$ . For the sequence 18, 24, 30, 36, the 18th term is $$a_{18} = 18 + (18 - 1)6 = 18 + 102 = 120$$ .

The common difference is 3, found by subtracting any two consecutive terms, e.g., 9 - 6 = 3.

The next term is 21, found by adding the common difference (3) to the last term (18).

A linear relationship can be represented in the form $$y = mx + b$$ , where $$m$$ is the slope and $$b$$ is the y-intercept.