If in the expansion of (a + b)ⁿ and (a + b)ⁿ + 3, the ratio of the coefficients of second and third terms, and third and fourth terms respectively are equal, then n is
(a) 3
(b) 4
(c) 5
(d) 6

Open in App

Solution

(c) n = 5

$Coefficients of the 2 nd and 3 rd terms in (a + b)^{n} are {}^{n}C_{1} and {}^{n}C_{2} Coefficients of the 3 rd and 4 th terms in (a + b)^{n + 3} are {}^{n + 3}C_{2} and {}^{n + 3}C_{3} Thus, we have \frac{{}^{n}C_{1}}{{}^{n}C_{2}} = \frac{{}^{n + 3}C_{2}}{{}^{n + 3}C_{3}} \Rightarrow \frac{2}{n - 1} = \frac{3}{n + 1} \Rightarrow 2 n + 2 = 3 n - 3 \Rightarrow n = 5$

Suggest Corrections

Similar questions

If in the expansion of $(a + b)^{n}$ and $(a + b)^{n + 3}$ , the ratio of the coefficients of second and third terms, and third and fourth terms respectively are equal, then n is

Q. If the second, third and fourth terms in the expansion of

{(a + b)}^{n}

are

135, 30

and

\frac{10}{3}

respectively, then

Q. If

T_{2} / T_{3}

in the expansion of

{(a + b)}^{n} and T_{3} / T_{4}

in the expansion of

{(a + b)}^{n + 3}

are equal, then n =
(a) 3
(b) 4
(c) 5
(d) 6

Q. In the expansion of

(a + b)^{n}

, the ratio of the binomial coefficients of

2^{n d}

and

3^{r d}

terms is equal to the ratio of the binomial coefficients of

5^{t h}

and

4^{t h}

terms, then

n =

Q. If the coefficients of second, third and fourth terms in the expansion of

(1 + x)^{n}

are in AP, then

n

is equal to:

Join BYJU'S Learning Program

If in the expansion of (a + b)n and (a + b)n + 3, the ratio of the coefficients of second and third terms, and third and fourth terms respectively are equal, then n is (a) 3 (b) 4 (c) 5 (d) 6

(c) n = 5 Coefficients of the 2nd and 3rd terms in (a+b)n are C1n and C2nCoefficients of the 3rd and 4th terms in (a+b)n+3 are C2n+3 and C3n+3Thus, we haveC1nC2n=C2n+3C3n+3⇒2n-1=3n+1⇒2n+2=3n-3⇒n=5

If in the expansion of (a + b)ⁿ and (a + b)ⁿ + 3, the ratio of the coefficients of second and third terms, and third and fourth terms respectively are equal, then n is
(a) 3
(b) 4
(c) 5
(d) 6