In the expansion of (1+a x)^ n , the first three terms are respectively 1,12 x and 64 x^2 . What is n equal to?

Step-by-step solution

The first three terms in expansion of (1+ ax )^ n are ^n C₀, ^n C₁ a x, ^n C₂ a^2 x^2 Given, ^n C₀=1 ; ^n C₁ a x=12 x ; ^n C₂ a^2 x^2=64 x^2 aligned & nax =12 x ; n(n-1) 2 a^2=64 & na =12 a= 12 n & n(n-1) 2 a^2=64 n(n-1) 2 144 n^2 =64 & n-1 n = 64 2 144 = 8 9 & n =9 aligned