# The first term of geometric sequence is 512 and the common ratio is 0.5 what is the 8th term of the sequence?

May 14, 2018

The ${8}^{t h} t e r m$ of the seqn, is : ${a}_{8} = 4$

#### Explanation:

We know that,

the ${n}^{t h} t e r m$ of geometric sequeence is:

${a}_{n} = {a}_{1} {r}^{n - 1}$

where ${a}_{1}$ is first term and $r$ is common ratio.

We have, ${a}_{1} = 512 \mathmr{and} r = 0.5 = \frac{1}{2}$

So, the ${8}^{t h} t e r m$ of the seqn, is :

${a}_{8} = {a}_{1} {\left(r\right)}^{8 - 1}$

$\therefore {a}_{8} = 512 {\left(\frac{1}{2}\right)}^{7} = 512 \times \frac{1}{128} = 4$