# What is the 7th term of the geometric sequence where a1 = -2 and a5 = -512?

Dec 6, 2015

$q = + 4 R i g h t a r r o w {a}_{6} = - 2048$
$q = - 4 R i g h t a r r o w {a}_{6} = + 2048$

#### Explanation:

${a}_{n} = {a}_{0} \cdot {q}^{n}$

${a}_{1} = {a}_{0} q = - 2$

${a}_{5} = {a}_{0} {q}^{5} = - 512$

${a}_{5} / {a}_{1} = {q}^{4} = \frac{- 512}{- 2} = 256 = {2}^{8}$

q = ± 4

a_1 = a_0 (±4) = -2 Rightarrow a_0 = ± (- 1/2)

a_6 = a_5 * q = -512 * (±4) = ± (- 2048)