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Powers with Positive and Negative Exponents

If a^n+2 = a^...

Question

If $a^{n + 2}$ = $a^{2 n - 1}$ , the value of n is :

A

1

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B

2

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C

3

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D

0

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Solution

The correct option is C
3

Given that $a^{n + 2}$ = $a^{2 n - 1}$
Since bases are equal, exponents must also be equal.
$\Rightarrow n + 2 = 2 n - 1$
$\Rightarrow 2 + 1 = 2 n - n$
$\Rightarrow n = 3$

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If $a^{n + 2}$ = $a^{2 n - 1}$ , the value of n is :

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\frac{a_{1} + a_{2 n}}{\sqrt{a_{1}} + \sqrt{a_{2}}} + \frac{a_{2} + a_{2 n - 1}}{\sqrt{a_{2}} + \sqrt{a_{3}}} + \frac{a_{3} + a_{2 n - 2}}{\sqrt{a_{3}} + \sqrt{a_{4}}} + . . . + \frac{a_{n} + a_{n + 1}}{\sqrt{a_{n}} + \sqrt{a_{n + 1}}} =

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