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Algebra

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- Sequences and Series

Still Confused?

Try reviewing these fundamentals first

Algebra

Arithmetic sequencesStill Confused?

Try reviewing these fundamentals first

Algebra

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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

• 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

• 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.

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