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  • If the 10th term of an A.P. is    and its 20th term is <img alt="\frac{1}{10}" src="http://entrancecorner.oncodecogs.com/gif.latex

If the 10th term of an A.P. is  \frac{1}{20}  and its 20th term is \frac{1}{10}, then the sum of its first 200 term is :
Option: 1 50\frac{1}{4}
Option: 3 100
Option: 5 50
Option: 7 100\frac{1}{2}
 

Answers (1)

best_answer

General Term of an AP

nth term (general term) of the A.P. is \mathrm{\mathit{a_n=a+(n-1)d}}.

Sum of n terms of an AP

The sum, Sn  of n terms of an AP with the first term ‘a’ and common difference ‘d’ is given by  

 

\begin{array}{l}{S_{n}=\frac{n}{2}[2 a+(n-1) d]} \\ {\text { OR }} \\ {S_{n}=\frac{n}{2}[a+l]} \\ {a \rightarrow \text { first term }} \\ {d \rightarrow \text { common difference }} \\ {n \rightarrow \text { number of terms }}\end{array}

 

Now,

\\a_{10}=a+9d=1/20\\a_{20}=a+19d=1/10\\On\,\,subtracting\,\,them\,\,,we\,\,get\,\,d=1/200\\a+9/10=1/20\Rightarrow a=1/200\\S_{200}=\frac {200}{2}\left [2/200+(199)\times1/200 \right ]=\frac{201}{2}

Correct Option (4)

Posted by

vishal kumar

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