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The nth term of series $- 3 + 6 - 12 + 24 - 48 + ....$ is

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{(- 1)}^{n} {.3.2}^{n - 1}

1^{n} {.3.2}^{n - 1}

{3.2}^{n + 1}

{2.3}^{n - 1}

answer is A.

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Detailed Solution

- 3 + 6 - 12 + 24 - 48 + .........

$a = - 3$ , $r = \frac{6}{- 3} = - 2$

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

$= - 3 {(- 2)}^{n - 1}$

$= (- 3) {(- 2)}^{n - 1}$

$= 3 (- 1) . {(- 1)}^{n - 1} . {(2)}^{n - 1}$

$= 3. {(- 1)}^{n} . {(2)}^{n - 1}$

$= {(- 1)}^{n} {.3.2}^{n - 1}$

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