# What would the formula for the nth term be given 0.3, -0.06, 0.012, -0.0024, 0.00048, ...?

${a}_{n} = \setminus \frac{0.3}{{\left(- 5\right)}^{n - 1}}$

#### Explanation:

Given series: $0.3 , - 0.06 , 0.012 , - 0.0024 , 0.00048 \setminus \ldots$

has first term $a = 0.3$ & a common ratio $r$ is given as follows

$r = \setminus \frac{- 0.06}{0.3} = \setminus \frac{0.012}{- 0.06} = \setminus \ldots = - \frac{1}{5}$

Now, the $n$th term of above Geometric progression (GP) will be as follows

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

${a}_{n} = 0.3 {\left(- \frac{1}{5}\right)}^{n - 1}$

${a}_{n} = \setminus \frac{0.3}{{\left(- 5\right)}^{n - 1}}$

Jul 2, 2018

$\implies {n}^{t h} t e r m$ of the sequence is :

${a}_{n} = \left(0.3\right) {\left(- 0.2\right)}^{n - 1}$

#### Explanation:

Here, the given sequence is :

$0.3 , - 0.06 , 0.012 , - 0.0024 , 0.00048 , \ldots$

The first term $= {a}_{1} = 0.3$

The common ratio :

$r = \frac{- 0.06}{0.3} = \frac{0.012}{- 0.06} = \frac{- 0.0024}{0.012} = \frac{0.00048}{- 0.0024} = - 0.2$

This is the geometric sequence :

$\implies {n}^{t h} t e r m$ of the sequence is :

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

$\implies {a}_{n} = \left(0.3\right) {\left(- 0.2\right)}^{n - 1}$