A) \[{{50}^{\frac{1}{4}}}\]
B) \[50\]
C) \[100\]
D) \[{{100}^{\frac{1}{2}}}\]
Correct Answer: D
Solution :
\[\therefore \,\,\,\,\,\,\,\,a+9d=\frac{1}{20}\] ... (i) \[a+19d=\frac{1}{100}\] ?. (ii) \[\therefore \] By (ii)-(i) \[10d=\frac{1}{10}-\frac{1}{20}=\frac{10}{200}=\frac{1}{20}\] \[\Rightarrow \,\,\,\,\,d=\frac{1}{200}\] \[\Rightarrow \,\,\,\,\,a=\frac{1}{200}from\,\,(i)\] \[\therefore \,\,\,\,\,\,{{S}_{200}}=100\left[ 2\times \frac{1}{200}+\frac{199}{200} \right]\] \[=1+\frac{199}{2}=\frac{201}{2}\] \[=100\frac{1}{2}\]
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