If p + 1, 2P - 10, 1 - 4p2are 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
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
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 -\(\frac{4}{11}\)
Source: Myschool Past Questions Archive (Record #30708)