Geometric sequences

Lesson: 1a
3:39
Lesson: 1b
7:02
Lesson: 1c
4:35
Lesson: 2
6:59
Lesson: 3
9:57

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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,

Lessons

• 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, … .
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 $t_1,r,t_n$ for the sequences in which two terms are given:
$t_3=18$ , $t_6=486$

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.

Geometric sequences

Geometric sequences

Lessons

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Practice topics for Sequences and Series