Question

6. The value of p if x, 2x+p and 3x+6 are in A. P.

value of p= ----------------​

Answer 1

Required Answer :-

In an AP, the difference between any two consecutive terms is constant. Hence, it is known as constant difference (d).

That means, the difference between the first and second term = difference between the second and third term..

Or we can consider the opposite. The difference will remain constant throughout.

Hence :-

➛ 2nd - 1st = 3rd - 2nd

➛ 2x + p - x = 3x + 6 - (2x + p)

➛ x + p = 3x + 6 - 2x - p

➛ x + p = x - p + 6

➛ x + p - x + p - 6 = 0

➛ 2p - 6 = 0

➛ 2p = 6

➛ p = 3(Ans)

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Answer 2

Required Answer :-

In an AP, the difference between any two consecutive terms is constant. Hence, it is known as constant difference (d).