Geometric sequences
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- Geometric sequence formula
Consider the geometric sequence: 2, 6, 18, 54, … . - 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.
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Topic Notes
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:
tn=t1⋅rn−1
where, tn : nth term
t1 : first term
r : common ratio
• the nth term, tn ,of a geometric sequence:
tn=t1⋅rn−1
where, tn : nth term
t1 : first term
r : common ratio
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