Find n, if n - 2, 4n - 1 and 5n + 2 are in AP

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Solution

As n - 2, 4n - 1, 5n + 2 are in A.P
$\Rightarrow 2 (4 n - 1) = n - 2 + 5 n + 2 \Rightarrow 8 n - 2 = 6 n \Rightarrow 2 n = 2 \Rightarrow n = 1$

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