JEE Main 2024 Mathematics question
Let three real numbers a, b, c be in arithmetic progression and a + 1, b, c + 3 be in geometric progression. If a > 10 and the arithmetic mean of a, b and c is 8, then the cube of the geometric mean of a, b and c is
Answer: (A)
Solution
b = 8, a = 8 − d, c = 8 + d; (9 − d)(11 + d) = 64 ⇒ d = −7 or 5; a > 10 gives d = −7, so a = 15, c = 1 and (GM)³ = abc = 120.