# How do you find nth term rule for a_2=28 and a_5=-1792?

Aug 17, 2016

${a}_{n} = - 7 {\left(- 4\right)}^{n - 1}$

#### Explanation:

The difference between the number implies this is a GP.

${a}_{5} = a {r}^{4} = - 1792$
${a}_{2} = a r = 28$

Divide the terms: ${a}_{5} / {a}_{2} = \frac{a {r}^{4}}{a r} = \frac{- 1792}{28}$

$\frac{\cancel{a} {r}^{4}}{\cancel{a} r} = - 64$

${r}^{3} = - 64$

$r = - 4$

${a}_{1} = \frac{28}{- 4} = - 7$

$\therefore {a}_{n} = - 7 {\left(- 4\right)}^{n = 1}$