What is the 9th term of the geometric sequence –1, 3, –9, …?

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What is the 9th term of the geometric sequence –1, 3, –9, …?

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Answer 1 · 2016-01-06T06:18:09

$a_{9} = - 6561$ $a_9=-6561$

Explanation:

$\frac{a_{2}}{a_{1}} = \frac{3}{- 1} = - 3$ $a_2/a_1=3/-1=-3$

$\frac{a_{3}}{a_{2}} = - \frac{9}{3} = - 3$ $a_3/a_2=-9/3=-3$

$\Rightarrow$ $implies$ common ratio $= r = - 3$ $=r=-3$ and $a_{1} = - 1$ $a_1=-1$

We know that:
$a_{n} = a_{1} r^{n - 1}$ $a_n=a_1r^(n-1)$
$\Rightarrow a_{9} = (- 1) {(- 3)}^{9 - 1} = (- 1) {(- 3)}^{8} = (- 1) 6561 = - 6561$ $implies a_9=(-1)(-3)^(9-1)=(-1)(-3)^8=(-1)6561=-6561$
$\Rightarrow a_{9} = - 6561$ $implies a_9=-6561$

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What is the 9th term of the geometric sequence –1, 3, –9, …?

1 Answer

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