Write the value of x for which

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Question:
Write the value of x for which (x + 2), 2x, (2x + 3) are three consecutive terms of an AP?

Solution:

Since (x + 2), 2x and (2x + 3) are in AP, we have:

$2 x-(x+2)=(2 x+3)-2 x$

$\Rightarrow x-2=3$

$\Rightarrow x=5$

$\therefore x=5$