Geometric Sequences

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 ratio is the factor by which each term in a geometric sequence is multiplied to get the next term.

The explicit formula for a geometric sequence can be written as: $$t(n) = a \times r^{(n-1)}$$ , where 'a' is the first term, 'r' is the common ratio, and 'n' is the term number.

The common ratio is 3, since each term is multiplied by 3 to get the next term.

The 4th term is 54.

The 5th term is 405.

The next three terms are 64, 32, 16.

The explicit equation is $$t(n) = 10 \times 2^{(n-1)}$$ .

The 6th term is 972.

The next three terms are 324, 972, 2916.