For any positive integer $n$ , let $n^{o}$ be defined by $n^{o} = 2 n (n + 1)$ . What is the value of $\frac{8^{o}}{2^{o}}$ ?

2^{o}

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4^{o}

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6^{o}

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8^{o}

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12^{o}

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Solution

The correct option is A $2^{o}$
Given,
$n^{o} = 2 n (n + 1)$
To find, $\frac{8^{o}}{2^{o}}$
$8^{o} = 2.8 (8 + 1) = 2.8.9 = 144$
$2^{o} = 2.2 (2 + 1) = 2.2.3 = 12$
$\frac{8^{o}}{2^{o}} = \frac{144}{12} = 12$
Value of $\frac{8^{o}}{2^{o}}$ $=$ $2^{o}$ $= 12$

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