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 non-zero and fixed number (a common ratio).
• geometric sequence: a sequence with a common ratio between successive terms.
• the nth term, tn ,of a geometric sequence:
where, tn : nth term
t1 : first term
r : common ratio
Geometric sequence formula
Consider the geometric sequence: 2, 6, 18, 54, … .
Identify the common ratio.
Determine the sixth term of the sequence.
Which term in the sequence has a value of 39366?
Determine t1,r,tn for the sequences in which two terms are given: t3=18, t6=486
Three consecutive terms of a geometric sequence are written in the form 5(x+2),8−x,x−2
Find the common ratio and the possible value of each of the three terms.