Maths · General term and middle term and simple applications
If the middle term in the expansion of ^{n} \) is then
If the middle term in the expansion of \( \left(x^{2}+\frac{1}{x}\right)^{n} \) is \( 924 x^{6}, \) then \( n= \)
- A. 10
- B. 12
- C. 14
- D. none of these
Step-by-step solution
Middle term occurs when n is even, r = n/2. General term: T_{r+1} = C(n, r) x^{2n-3r}. For middle term, exponent of x is 6, so 2n - 3(n/2) = n/2 = 6 ⇒ n = 12. Then coefficient = C(12, 6) = 924, which matches given coefficient. Thus n = 12.
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