If p + 1, 2P – 10, 1 – 4p

^{2}are three consecutive terms of an arithmetic progression, find the possible values of p-
**A.**

-4, 2 -
**B.**

-3, (frac{4}{11}) -
**C.**

-(frac{4}{11}), 2 -
**D.**

5, -3

##### Correct Answer: Option C

##### Explanation

2p – 10 = (frac{p + 1 + 1 – 4P^2}{2}) (Arithmetic mean)

= 2(2p – 100 = p + 2 – 4P^{2})

= 4p – 20 = p + 2 – 4p^{2}

= 4p^{2} + 3p – 22 = 0

= (p – 2)(4p + 11) = 0

∴ p = 2 or -(frac{4}{11})