Geometric sequences  Sequences and Series
Geometric sequences
A geometric sequence, also called geometric progression, is a number sequence with a common ratio between successive terms. A term in a geometric sequence can be found by multiplying the previous one by a nonzero and fixed number (a common ratio).
Basic concepts:
 Arithmetic sequences
Lessons
Notes:
• geometric sequence: a sequence with a common ratio between successive terms.
• the nth term, ${t_n}$ ,of a geometric sequence:
${t_n}\; = \;{t_1} \cdot {r^{n  1}}$
where, ${t_n}$ : nth term
${t_1}$ : first term
r : common ratio

1.
Geometric sequence formula
Consider the geometric sequence: 2, 6, 18, 54, … .