Geometric and Arithmetic Sequences

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

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

The common difference (d) can be found by subtracting any term from the subsequent term: d = a_{n+1} - a_n.

The common ratio (r) can be found by dividing any term by the previous term: r = a_{n+1} / a_n.

The explicit formula for an arithmetic sequence is $$a_n = a_1 + (n-1)d$$ , where a_1 is the first term and d is the common difference.

The explicit formula for a geometric sequence is $$a_n = a_1 \times r^{(n-1)}$$ , where a_1 is the first term and r is the common ratio.

The sequence is geometric.

The sequence is arithmetic.

The sequence is arithmetic.

The common difference is 5.