# What is the 10th term of this geometric sequence 1, 2, 4, 8, …?

Aug 10, 2015

color(blue)(T_10= 512

#### Explanation:

the geometric sequence given is:
$1 , 2 , 4 , 8$ ...

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

2) $\frac{4}{2} = 2$

for this sequence the common ratio $r = 2$ the first term $a = 1$

The 10th term can be obtained through formula:

$\textcolor{b l u e}{{T}_{n} = a {r}^{n - 1}} = 1 \times {2}^{\left(10 - 1\right)}$ , where $n$ = 10

${T}_{10} = 1 \times {2}^{9}$

color(blue)(T_10= 1 xx 512= 512