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Question

Write the value of $$x$$ for which $$x+2,\ 2x,\ 2x+3$$ are three consecutive terms of an A.P


Solution

Given,

$$x+2,2x,2x+3$$ are in A.P.

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

$$2x-x-2=2x+3-2x$$

$$x-2=3$$

$$\therefore x=5$$

The consecutive numbers are : $$5+2,2(5),2(5)+3$$

$$\Rightarrow 7,10,13$$

Mathematics

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