# If first term of a G.P. is 1024 and fourth term is -16, which of the following is seventh term?

## A. $2$ B. $- 0.25$ C. $4$ D. $- 8$

Mar 20, 2017

B. $- 0.25$

#### Explanation:

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

${a}_{4} = {a}_{1} \cdot {r}^{4 - 1}$

$- 16 = 1024 \cdot {r}^{3}$

$- \frac{16}{1024} = {r}^{3}$

$- \frac{1}{64} = {r}^{3}$

$- \frac{1}{4} = r$

therefore,
${a}_{7} = 1024 \cdot {\left(- \frac{1}{4}\right)}^{7 - 1}$

$= 1024 \cdot {\left(- \frac{1}{4}\right)}^{6}$

$= {4}^{5} \cdot {\left(- \frac{1}{4}\right)}^{6} = - \frac{1}{4} = - 0.25$