First slide

Binomial theorem for positive integral Index

Question

The two successive terms in the expansion of (1 + x)²⁴ whose coefficients are in the ratio 1:4 are

Moderate

A

3rd and 4th
B

4th and 5th
C

5th and 6th
D

6th and 7t}r

Solution

Given expression is $(1 + x)^{24}$ Let two successive terms are (r + 1)th and (r + 2)th
terms $\Rightarrow T_{r + 1} =^{24} C_{r} x^{r} and T_{r + 2} =^{24} C_{r + 1} x^{r + 1}$
Now, ratio of coefficients = 1
$\begin{aligned} \Rightarrow \frac{^{24} C_{r}}{^{24} C_{r + 1}} = \frac{1}{4} \Rightarrow \frac{r + 1}{24 - r} = \frac{1}{4} \\ \Rightarrow 4 r + 4 = 24 - r \Rightarrow r = 4 \end{aligned}$
.'. Required terms are 5th and 6th.

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App