Find the middle term in the expansion of-i 23 x-32 - 20ii a x-b x 12iii - 2-2 - 10iv xa-ax 10

(i) Here, n = 20 nbsp; (Even number) nbsp; Therefore, the middle term is the n2+1th term, i.e., the 11th term. Now,T11=T10+1=C1020 #160; #160;23x20 10 ...

You visited us 5 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

Sequence

Find the midd...

Question

Find the middle term in the expansion of:
(i) ${(\frac{2}{3} x - \frac{3}{2 x})}^{20}$

(ii) ${(\frac{a}{x} + b x)}^{12}$

(iii) ${(x^{2} - \frac{2}{x})}^{10}$

(iv) ${(\frac{x}{a} - \frac{a}{x})}^{10}$

Open in App

Solution

(i) Here,
n = 20 (Even number)
Therefore, the middle term is the $(\frac{n}{2} + 1)$ th term, i.e., the 11th term.
$Now, T_{11} = T_{10 + 1} = {}^{20}C_{10} {(\frac{2}{3} x)}^{20 - 10} {(\frac{3}{2 x})}^{10} = {}^{20}C_{10} \frac{2^{10}}{3^{10}} \times \frac{3^{10}}{2^{10}} x^{10 - 10} = {}^{20}C_{10}$

(ii) Here,
n = 12 (Even number)
Therefore, the middle term is the $(\frac{n}{2} + 1) th$ i.e. 7th term
$Now, T_{7} = T_{6 + 1} = {}^{12}C_{6} {(\frac{a}{x})}^{12 - 6} (b x)^{6} = {}^{12}C_{6} a^{6} b^{6} = \frac{12 \times 11 \times 10 \times 9 \times 8 \times 7}{6 \times 5 \times 4 \times 3 \times 2} a^{6} b^{6} = 924 a^{6} b^{6}$

(iii) Here,
n = 10 (Even number)
Therefore, the middle term is the $(\frac{n}{2} + 1) th$ i.e. 6th term
$Now, T_{6} = T_{5 + 1} = {}^{10}C_{5} (x^{2})^{10 - 5} {(\frac{- 2}{x})}^{5} = - \frac{10 \times 9 \times 8 \times 7 \times 6}{5 \times 4 \times 3 \times 2} \times 32 x^{5} = - 8064 x^{5}$

(iv) Here,
n = 10 (Even number)
Therefore, the middle term is the $(\frac{n}{2} + 1) th$ i.e. 6th term
$Now, T_{6} = T_{5 + 1} = {}^{10}C_{5} {(\frac{x}{a})}^{10 - 5} {(\frac{- a}{x})}^{5} = - \frac{10 \times 9 \times 8 \times 7 \times 6}{5 \times 4 \times 3 \times 2} = - 252$

Suggest Corrections

Similar questions

Q. Find the middle terms(s) in the expansion of:
(i)

{(x - \frac{1}{x})}^{10}

(ii)

{(1 - 2 x + x^{2})}^{n}

(iii)

{(1 + 3 x + 3 x^{2} + x^{3})}^{2 n}

(iv)

{(2 x - \frac{x^{2}}{4})}^{9}

(v)

{(x - \frac{1}{x})}^{2 n + 1}

(vi)

{(\frac{x}{3} + 9 y)}^{10}

(vii)

{(3 - \frac{x^{3}}{6})}^{7}

(viii)

{(2 a x - \frac{b}{x^{2}})}^{12}

(ix)

{(\frac{p}{x} + \frac{x}{p})}^{9}

(x)

{(\frac{x}{a} - \frac{a}{x})}^{10}

Q. Find the middle terms in the expansion of:
(i)

{(3 x - \frac{x^{3}}{6})}^{9}

(ii)

{(2 x^{2} - \frac{1}{x})}^{7}

(iii)

{(3 x - \frac{2}{x^{2}})}^{15}

(iv)

{(x^{4} - \frac{1}{x^{3}})}^{11}

Find the middle term in the expansion of:

$(i) {(\frac{2}{3} x - \frac{3}{2 x})}^{20}$

$(i i) {(\frac{a}{x} + b x)}^{12}$

$(i i i) {(x^{2} - \frac{2}{x})}^{10}$

$(i v) {(\frac{x}{a} - \frac{a}{x})}^{10}$

Find the middle term in the expansion of:

$(i) {(3 x - \frac{x^{3}}{6})}^{9}$

$(i i) {(2 x^{2} - \frac{1}{x})}^{7}$

$(i i i) {(3 x - \frac{2}{x^{2}})}^{15}$

$(i v) {(x^{4} - \frac{1}{x^{3}})}^{11}$

Q. The middle term in the expansion of

{(a x - \frac{b}{x^{2}})}^{12}

is:

Join BYJU'S Learning Program

Find the middle term in the expansion of: (i) 23x-32x20 (ii) ax+bx12 (iii) x2-2x10 (iv) xa-ax10

Find the middle term in the expansion of:
(i) ${(\frac{2}{3} x - \frac{3}{2 x})}^{20}$

(ii) ${(\frac{a}{x} + b x)}^{12}$

(iii) ${(x^{2} - \frac{2}{x})}^{10}$

(iv) ${(\frac{x}{a} - \frac{a}{x})}^{10}$