The formula for any geometric sequence is an = a1 · rn - 1, where an represents the value of the nth term, a1 represents the value of the first term, r represents the common ratio, and n represents the term number. What is the formula for the sequence 2, -6, 18, -54, ...?
an = 2 · 3 n - 1
an = 2 · (-3) n - 1
an = -3 · 2 n - 1
an = 3 · 2 n - 1

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joaobezerra joaobezerra · Answer 1 · 2021-01-17T01:04:49+01:00

Answer:

The formula for the sequence is: [tex]a_n = 2*(-3)^{n-1}[/tex]

Step-by-step explanation:

The general term of a geometric sequence is given by:

[tex]a_n = a_1*r^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term and r is the common ratio between the terms, that is, the division between them.

What is the formula for the sequence 2, -6, 18, -54, ...?

First term is 2, so [tex]a_1 = 2[/tex]

Common ratio is given by:

[tex]r = \frac{-6}{2} = \frac{18}{-6} = ... = -3[/tex]

So the sequence is given by:

[tex]a_n = 2*(-3)^{n-1}[/tex]