If $2 x, x + 10, 3 x + 2$ are in AP, find the value of x

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Solution

Given 2x,x+10, 3x+2 ar in AP then common difference in common = $2^{n d}$ term - previous term
$x + 10 - 2 x = 3 x + 2 - x - 10$
$- x + 10 = 2 x - 8$
$3 x = 18$
$[x = 6]$
Hence x=6 for given terms are in AP.

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