The coefficients of three consecutive terms of `(1+x)^(n+5)` are in the ratio 5:10:14. Then `n=` ___________.

Options

A. 5
B. 7
C. 6
D. 8

Answer

C

Explanation

Let `t^(th), (r +1)^(th) and (r +2)^(th)` be three consecutive
terms in the expansion of `(1 + x)^(n+5)`. It is given that
`""^(n+5)C_(r-1) :""^(n+5)C_(r) :""^(n+5)C_(r+1) = 5:10:14`
`rArr (""^(n+5)C_(r))/ (""^(n+5)C_(r-1)) =(10)/(5) and (""^(n+5)C_(r+1))/(""^(n+5)C_(r)) =(14)/(10)`
`rArr (n+5 - r +1)/(r) = 2 and ((n+5) -r)/(r+1) = (7)/(5)`
`rArr n- 3r + 6 = 0 and 5n - 12r + 18 = 0`
`rArr n = 6 , r = 4`