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General Form of an AP

If x+2, 2 x,2...

Question

If $(x + 2), 2 x, (2 x + 3)$ are three consecutive terms of an AP, find the value of x.

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Solution

If (x+2),2x and (2x+3) are three consecutive terms of an AP, then we have:
2x - (x+2) = (2x+3) - 2x
⇒ x - 2 = 3
⇒ x = 5
Hence, the value of x is 5.

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