MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Middle Terms

The sum of th...

Question

The sum of the coefficients in the first three terms of the expansion of ${(x^{2} - \frac{2}{x})}^{m}$ is equal to $97$ . Find the term of the expansion containing $x^{4}$ .

Open in App

Solution

Sum of first three terms be $^{m} C_{0} - 2^{m} C_{1} + 4^{m} C_{2} = 97$
$⟹ 1 - 2 m + 2 (m) (m - 1) = 97 ⟹ 2 m^{2} - 4 m - 96 = 0 ⟹ m^{2} - 2 m - 48 = 0 ⟹ m = 8, - 6$
$m$ can't be negative so $m = 8$
General term is $^{8} C_{r} (x^{16 - 2 r}) (\frac{- 2}{x})^{r}$
$16 - 3 r = 4 ⟹ r = 4$
The term of expansion containing $x^{4}$ is $^{8} C_{4} (2)^{4} x^{4}$

Suggest Corrections

thumbs-up

0

Similar questions

Q. The sum of the coefficients in the first, second, and third terms of the expansion of

{(x^{2} + \frac{1}{x})}^{m}

46

. Find the term of the expansion which does not contain

x

Q. If the sum of the coefficients of the first, second and third terms of the expansion of

{(x^{2} + \frac{1}{x})}^{m}

46

, then the coefficient of the term that does not contain

x

Q. The sum of the coefficients of the first three terms in the expansion of

{(x - \frac{3}{x^{2}})}^{m}, x \neq 0

m

being a natural number is ,

559

. Find the term of the expansion containing

x^{3}

Q. The sum of the coefficients of first three terms in the expansion of

{(x - \frac{3}{x^{2}})}^{m}, x \neq 0

m

being a natural number, is

559

. Find the term of the expansion containing

x^{3}

Q. The sum of the coefficient of first 3 terms in the expansion

{(x - \frac{3}{x^{2}})}^{m}

in 559 . Find the term of the expansion containing

x^{3}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Visualising the Terms

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon