Question

Find the 9th term of the following geometric sequence 1 -3 9 -27

Answer 1

Answer: The 9th term is 6561

Step-by-step explanation:

The geometric sequences have the following formula

$a_n = a_1(r)^{n-1}$

Where $a_1$ is the first term of the sequence and r is the common ratio between the consecutive terms of the sequence

In this case the sequence is   1 -3 9 -27

So $a_1 = 1$

Observe that the common ratio  r is:

$r=\frac{-3}{1}=\frac{9}{3}=\frac{-27}{9}=-3$

So the formula is:

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

We want to find $a_9$

$a_9 = (-3)^{9-1}$

$a_9 = (-3)^{8}=6561$