If p + 1, 2P – 10, 1 – 4p2are three consecutive terms of an…

If p + 1, 2P – 10, 1 – 4p²are three consecutive terms of an arithmetic progression, find the possible values of p

Correct Answer: Option C

Explanation

2p – 10 = (frac{p + 1 + 1 – 4P^2}{2}) (Arithmetic mean)
= 2(2p – 100 = p + 2 – 4P²)
= 4p – 20 = p + 2 – 4p²
= 4p² + 3p – 22 = 0
= (p – 2)(4p + 11) = 0
∴ p = 2 or -(frac{4}{11})