Question

Find $p$ if the $4^{th}$ term is $\frac{5}{2}$

• A. $0.5$
• B. $0.3$
• C. $0.25$
• D. $4$

Answer 1

The correct option is A $0.5$

Given that: $T_4=\frac{5}{2}$

Solution:

$4^{th}$ term i.e. $T_4$ in the expansion of ${(px+\frac{1}{x})}^n={}^n{C}_3\times (px{)}^3\times {\left(\frac{1}{x}\right)}^{n-3}$

Now, $T_4$$={}^n{C}_3\times (px{)}^3\times {\left(\frac{1}{x}\right)}^{n-3}$

or, $T_4$$={}^n{C}_3\times p^3\times x^{6-n}$

Since, $T_4$ is indepemdent of $x.$

So, power of $x$ i.e. $6-n$ should be zero.

or, $6-n=0$

or, $n=6$

Now, $T_4={}^6{C}_3\times p^3=\frac{5}{2}$

or, $20\times p^3=\frac{5}{2}$

or, $p=\frac{1}{2}=0.5$

Hence, A is the correct option.