If the 10 th term of an A.P. is 1 20 and its 20 th term is 1 10 , then the sum of its first 200 terms is

Question

If the $10^{th}$ term of an A.P. is $\frac{1}{20}$ and its $20^{th}$ term is $\frac{1}{10}$ , then the sum of its first 200 terms is

Smart Achievers · Accepted Answer

(4)

$Given, T_{10} = \frac{1}{20} = a + 9 d$ ...(i)

$and$ $T_{20} = \frac{1}{10} = a + 19 d$ ...(ii)

$Solving (i) and (ii), we have$

$a = \frac{1}{200},$ $d = \frac{1}{200}$

$∴$ $S_{200} = \frac{200}{2} [\frac{2}{200} + \frac{199}{200}] = \frac{201}{2} = 100 \frac{1}{2}$

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