Arithmetic Sequences and Series

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 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.

The common difference is 3, as each term increases by 3.

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

The 10th term is 29.

The formula for the sum of an arithmetic series is: $$S_n = \frac{n}{2}(2a_1 + (n-1)d)$$ , where $$d$$ is the common difference.

The common difference is -3.

The 5th term is 34.

2, 4, 8, 16, ... is NOT an arithmetic sequence.

The sum is 100.