Question

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

Answer 1

The solution is given below :-

Answer 2

n = 6

Step-by-step explanation:

Let the three consecutive ternms are$T_r,T_r_+_1,T_r_+_2$

$T_r=^n^+^5C_r,$

$T_r_+_1=^n^+^5C_r_+_1$

$T_r_+_2 = ^n^+^5C_r_+_2$

Ratio of coefficient of these terms = 5:10:14

Now, $\frac{^n^+^5C_r}{^n^+^5C_r_+_1} = \frac{5}{10}$

⇒n-3r = -3......(1)

Also,

$\frac{^n^+^5C_r_+_1}{^n^+^5C_r_+_2}=\frac{10}{14}$

⇒5n-12r= - 6.....(2)

Multiply eqtion (1) by 4,

4n-12r= - 12

From equation (1) and (2)

5n-12r-(4n-12r)= - 6+12

n= 6

Also,from (1),

r = 3.

Hence,n = 6