Question

The ratio of three consecutive terms in expansion of (1 + x)^n+5 is 5:10: 14, then the greatest coefficient is

Answer 1

"The ratio of three consecutive terms in expansion of (1 + x)^n+5 is 5:10: 14, then the greatest coefficient is. StrongGirl is waiting for your help."

Answer 2

Answer:

Answer:–

• The greatest coefficient =462

✍ Given:–

• The ratio of three consecutive terms in expansion ${(1 + x)}^{n + 5}$ is 5:10:14.

To find:–

• The greatest coefficient=?

✍ solution:–

Let the coefficients of three consecutive terms of

${(1 + x)}^{n + 5}$ be

$^{n + 5}c( {r - 1}), ^{n + 5} c(r), ^{n + 5} c(r + 1)$

The ratio is,

$^{n + 5}c(r -1): ^{n + 5} c(r): ^{n + 5} c(r + 1) = 50:10:14$

$\frac{^{n + 5}c(r - 1)}{ ^{n + 5}c(r) } = \frac{5}{10}$

$\frac{r}{n + 6 - r} = \frac{1}{2}$

$n - 3r + 6 = 0 ➟1$

And,

$\frac{ ^{n + 5}c(r)}{ ^{n + 5}c(r + 1) } = \frac{5}{7}$

$\frac{r + 1}{n - r + 5} = \frac{5}{7}$

$5n - 12r + 18 = 0 ➟2$

Solve Equation 1 and 2

We get

n=6

From this,

The greatest coefficient=¹¹C5=462