# What is the 7th term of the geometric sequence 4, –20, 100, …?

May 19, 2018

color(maroon)(a_7 = 4 * (-5)^6 = 62500

#### Explanation:

$a = 4 , {a}_{2} = - 20 , {a}_{3} = 100$. To find ${a}_{7}$

Common ratio $r = {a}_{2} / a = {a}_{3} / {a}_{2} = - \frac{20}{4} = \frac{100}{-} 20 = - 5$

${n}^{t h}$ term of G S ${a}_{n} = a {r}^{n - 1}$

$\therefore {a}_{7} = a \cdot {r}^{6}$

color(maroon)(a_7 = 4 * (-5)^6 = 62500