# What is the 8th term of the geometric sequence 3, 9, 27,...?

May 20, 2015

The geometric sequence given is:
$3 , 9 , 27$ ...

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:

• common ratio $r = 3$
• first term $a = 3$
• $n = 8$

The 8th term can be obtained through formula
${T}_{n} = a {r}^{n - 1} = 3 \times {3}^{\left(8 - 1\right)}$
$= 3 \times {3}^{7}$
$= 3 \times 2187 = 6561$