# How do you write an nth term rule for 6,-30,150,-750,... and find a_6?

Sep 30, 2016

The n^(th) term ${a}_{n} \text{ is } 6 {\left(- 5\right)}^{n - 1} , \mathmr{and} , {a}_{6} = - 18750$#.

#### Explanation:

Let ${a}_{n}$ be the ${n}^{t h}$ term of the seq.

We observe that,

${a}_{2} / {a}_{1} = {a}_{3} / {a}_{2} = {a}_{4} / {a}_{3} = \ldots = - 5$

So, if this pattern continue, we can say that the seq. is a Geom. Seq.,

having the First Term ${a}_{1} = 6 ,$ and, the Common Ratio $r = - 5.$

For such a seq., ${a}_{n} = {a}_{1} \cdot {r}^{n - 1} = 6 {\left(- 5\right)}^{n - 1}$.

$\therefore {a}_{6} = 6 {\left(- 5\right)}^{5} = - 18750$