1.

If p, q, r are in A.P and p – r = q then  find the value of p in terms of q.1. \( p = \rm\frac{3q}{2}\)2. \( p = \rm\frac{2q}{3}\)3. \( p = \rm\frac{q}{3}\)4. \( p = \rm\frac{3q}{5}\)

Answer» Correct Answer - Option 1 : \( p = \rm\frac{3q}{2}\)

CONCEPT : 

  • If a, b, c are in AP, then by the rule of arithmetic mean we can write as \(b = \rm\frac{a + c}{2}\).

CALCULATION : 

As given p – r = q.

⇒ r = p - q . . . . . . . . . . . . .  (1)

And we know that \(q = \rm\frac{p + r}{2}\)

Putting the value of r from equation (1) to the above equation we get

\(\Rightarrow q = \rm\frac{p + (p -q)}{2}\)

On solving we get 3q = 2p

\(\Rightarrow p = \rm\frac{3q}{2}\)

Therefore, option (1) is the correct answer.


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