If the sum and product of the first three terms in an A.P are 33 and 1155 respectively, then a value of its 11th term is:

a-d + a + a+d = 33 ⇒ 3a = 33 ⇒ a = 11
a(a² - d²) = 1155
11(11² - d²) = 1155
121 - d² = 105
d² = 16 ⇒ d = ±4
If d = 4 then 1st term = 7
If d = -4 then 1st term = 15
T₁₁ = 7 + 40 = 47
OR
T₁₁ = 15 - 40 = -25