Question

If rth term is the middle term in the expansion of ${(x^2-\frac{1}{2x})}^{20}$, then $(r+3{)}^{th}$ term is

• A. ${}^{20}{C}_{14}\left(\frac{x}{2^{14}}\right)$
• B. ${}^{20}{C}_{12}{x}^2{2}^{-12}$
• C. ${-}^{20}{C}_{7}x{.2}^{-13}$
• D. None of these

Answer 1

The correct option is C

${-}^{20}{C}_{7}x{.2}^{-13}$

${-}^{20}{C}_{7}x{.2}^{-13}$

Here n is even

So, The middle term in the given expansion is $(\frac{20}{2}+1)th$ =11th term

Therefore, (r+3)th term is the 14th term

$T_{14}={}^{20}{C}_{13}(x^2{)}^{20-13}{\left(\frac{-1}{2x}\right)}^{13}$

$=(-1{)}^{13}{}^{20}{C}_{13}\frac{x^{14-13}}{2^{13}}$

$={-}^{20}{C}_{7}x{2}^{-13}$