Question #48769

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Question #48769

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Answer 1 · 2017-08-02T08:31:07

$24.5$ $24.5$

Explanation:

$a r^{n - 1} = a_{n}$ $ar^(n-1)=a_n$

$a r^{2} = 8$ $ar^2=8$
$a r^{4} = 14$ $ar^4=14$

$\frac{a r^{4}}{a r^{2}} = \frac{14}{8}$ $(ar^4)/(ar^2)=14/8$
$r^{2} = \frac{7}{4}$ $r^2=7/4$
$r = \sqrt{\frac{7}{4}}$ $r=sqrt(7/4)$

Method 1:
$a_{7} = a r^{6} = a r^{4} \cdot r^{2} = 14 \cdot \frac{7}{4} = 24.5$ $a_7=ar^6=ar^4*r^2=14*7/4=24.5$

Method 2:
$a r^{2} = 8$ $ar^2=8$
$a (\frac{7}{4}) = 8$ $a(7/4)=8$
$a = 8 \cdot (\frac{4}{7}) = 4.57142857$ $a=8*(4/7)=4.57142857$
$a r^{6} = 4.57142857 \cdot {(\sqrt{\frac{7}{4}})}^{6} = 24.5$ $ar^6=4.57142857*(sqrt(7/4))^6=24.5$

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Question #48769

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