The fifth term of an A.P is 24 and the eleventh term is 96. Find…

The fifth term of an A.P is 24 and the eleventh term is 96. Find the first term.

Correct Answer: Option D

Explanation

U₅ = 24, n = 5 and U₁₁ = 96, n = 11
U_n = a + (n-1)d
24 = a + (5-1)d imply 24 = a+4d …..eqn1
96 = a + (11-1)d imply 96 = a+10d …eqn2
eqn1 – eqn2 -72 = -6d
d = ⁷²/₆ = 12
but 24 = a+4d
24 = a + 4(12)
24 = a + 48
a = 24-48
a = -24