Question

${20}^{th}$ term in the binomial expansion of $(1+x{)}^{20}$ when $x=5$ is .

• A. $20\times 5^{19}$
• B. $10\times 5^{20}$
• C. $20\times 5^{20}$
• D. $10\times 5^{21}$

Answer 1

The correct option is A $20\times 5^{19}$

We want to find the ${20}^{th}$ term or $T_{20}$
We know $T_{r+1}={}^n{C}_r{x}^{n-r}{y}^r$ in the expansion of $(x+y{)}^n$
$T_{r+1}$ in the expansion of $(1+x{)}^{n}is{}^n{C}_r{x}^r$
$\Rightarrow T_{20}={}^{20}{C}_{19}{x}^{19}$
$=20\times 5^{19}$