# What is the 6th term of this geometric sequence 3, –9, 27, –81, …?

Jun 29, 2015

 color(blue)(-729

#### Explanation:

the geometric sequence given is:
$3 , - 9 , 27 , - 81$ ...

When provided with a geometric sequence we must first calculate the common ratio $r$
$r$ is obtained by dividing a term by its preceding term
1) $- \frac{9}{3} = - 3$
2) $\frac{27}{-} 9 = - 3$

for this sequence the common ratio $r = - 3$ the first term $a = 3$
and $n = 6$

The 6th term can be obtained through formula
${T}_{n} = a {r}^{n - 1} = 3 \times - {3}^{\left(6 - 1\right)}$
$= 3 \times - {3}^{5}$
= 3 xx -243= color(blue)(-729