How do you write a rule for the nth term of the geometric sequence and then find $a_{5}$ $a_5$ given $a_{3} = - 144, r = 0.5$ $a_3=-144, r=0.5$ ?

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How do you write a rule for the nth term of the geometric sequence and then find $a_{5}$ $a_5$ given $a_{3} = - 144, r = 0.5$ $a_3=-144, r=0.5$ ?

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Answer 1 · 2017-12-15T15:12:42

$a_{n} = - 576 {(0.5)}^{n - 1}, a_{5} = - 36$ $a_n=-576(0.5)^(n-1),a_5=-36$

Explanation:

$the nth term of a geometric sequence is$ $"the nth term of a geometric sequence is "$

$∙ x a_{n} = a r^{n - 1}$ $•color(white)(x)a_n=ar^(n-1)$

$where a is the first term and r the common ratio$ $"where a is the first term and r the common ratio"$

$a_{3} = a r^{2} = - 144$ $a_3=ar^2=-144$

$\Rightarrow a = - \frac{144}{0.25} = - 576 \leftarrow first term$ $rArra=-144/(0.25)=-576larrcolor(blue)"first term"$

$\Rightarrow a_{n} = - 576 {(0.5)}^{n - 1}$ $rArra_n=-576(0.5)^(n-1)$

$\Rightarrow a_{5} = - 576 \times {(0.5)}^{4} = - 36$ $rArra_5=-576xx(0.5)^4=-36$

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How do you write a rule for the nth term of the geometric sequence and then find $a_{5}$ $a_5$ given $a_{3} = - 144, r = 0.5$ $a_3=-144, r=0.5$ ?

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How do you write a rule for the nth term of the geometric sequence and then find a_5a5a_5 given a_3=-144, r=0.5a3=−144,r=0.5a_3=-144, r=0.5?

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Explanation:

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How do you write a rule for the nth term of the geometric sequence and then find $a_{5}$ $a_5$ given $a_{3} = - 144, r = 0.5$ $a_3=-144, r=0.5$ ?