# What is the 6th term of this geometric sequence 1, 7, 49, 343, …?

Jun 29, 2015

color(blue)(16807

#### Explanation:

the geometric sequence given is:
$1 , 7 , 49 , 343$ ...

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) $\frac{7}{1} = 7$
2) $\frac{49}{7} = 7$

for this sequence the common ratio $r = 7$ the first term $a = 1$
and $n = 6$

The 6th term can be obtained through formula
${T}_{n} = a {r}^{n - 1} = 1 \times {7}^{\left(6 - 1\right)}$
$= 1 \times {7}^{5}$
= 1 xx 16807= color(blue)(16807