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Geometric sequences
- Lesson: 1a3:39
- Lesson: 1b7:02
- Lesson: 1c4:35
- Lesson: 26:59
- Lesson: 39:57
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 non-zero and fixed number (a common ratio).
Basic Concepts: Arithmetic sequences
Related Concepts: Pascal's triangle, Binomial theorem, Introduction to sequences, Monotonic and bounded sequences
Lessons
• 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
- 1.Geometric sequence formula
Consider the geometric sequence: 2, 6, 18, 54, … .a)Identify the common ratio.b)Determine the sixth term of the sequence.c)Which term in the sequence has a value of 39366? - 2.Determine t1,r,tn for the sequences in which two terms are given:
t3=18, t6=486 - 3.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.