Arithmetic Sequences and Series

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

The common difference is the fixed amount that each term increases or decreases by in an arithmetic sequence.

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.

The 10th term is $$a_{10} = 5 + (10-1)3 = 32$$ .

The sum can be calculated using the formula: $$S_n = \frac{n}{2} (a_1 + a_n)$$ , where $$S_n$$ is the sum of the first n terms, $$a_1$$ is the first term, and $$a_n$$ is the nth term.

The common difference is -16.

The rule for the nth term is $$a_n = -63 + 4n$$ .

An arithmetic sequence has a common difference.

The fourth and fifth terms are 5/4 and 3/2.

The common difference is 5.