Question

If a, b, c be three natural numbers in A.P. and a + b + c = 21, then the possible number of values of a , b, c is-

• A. 15
• B. 14
• C. 13
• D. 16

Answer 1

Answer: (C)

13

Answer 2

Let b = a + d and c = a + 2d, then equation is

a + a + d + a + 2d = 21 Ž a + d = 7 \ a + c = 14 and b = 7

Now, the number of positive integral solutions of a + c = 14 is equal to coefficient of x¹⁴ in (x + x² + x³ +…….) = coefficient of x¹² in (1+ x + x²……)² = ¹³C₁₂ = 13