JEE Class main Answered

Let the coefficients of consecutive terms are

  ...............................(1)

  .....................(2)

  .......................(3)

From eqn.(1) and eqn.(2) , we get

from above expression, we get

(n-r+2) = 3 r + 3  

 n = 4 r + 1  ................................(4)

From eqn.(2) and eqn.(3) , we get

From above expression, we get

3(n-r+1)  = 5(r+2)

n = (8/3)r + (7/3)  ..........................(5)

By equating (4) and (5) and solving for r , we get r = 1

By substituting r =1 in eqn.(4) , we get n = 5

hence consecutive coefficients are  ⁷C₁ , ⁷C₂ and ⁷C₃

⁷C₁ + ⁷C₂ + ⁷C₃ = 7 + 21 + 35 = 63