Question

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

Answer 1

Answer:

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

Step-by-step explanation:

The general term of a geometric sequence is given by:

$a_n = a_1*r^{n-1}$

In which $a_1$ 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 $a_1 = 2$

Common ratio is given by:

$r = \frac{-6}{2} = \frac{18}{-6} = ... = -3$

So the sequence is given by:

$a_n = 2*(-3)^{n-1}$