If the 10th term of an A.P. is $${1 \over {20}}$$ and its 20th term is $${1 \over {10}}$$, then the sum of its first 200 terms is
JEE · Math · previous-year question
- A.100
- B.$$100{1 \over 2}$$correct
- C.$$50{1 \over 4}$$
- D.50
Answer
B. $$100{1 \over 2}$$
Explanation
T10 = a + 9d = $${1 \over {20}}$$ ....(1) T20 = a + 19d = $${1 \over {10}}$$ .....(2) Equation (2) – (1) 10d = $${1 \over {10}}$$ - $${1 \over {20}}$$ $$ \Rightarrow $$ d = $${1 \over {200}}$$ a + $${9 \over {200}}$$ = $${1 \over {20}}$$ $$ \Rightarrow $$ a = $${1 \over {200}}$$ S200 = $${{200} \over 2}\left[ {{2 \over {200}} + \left( {200 - 1} \right) \times {1 \over {200}}} \right]$$ = $$100\left[ {{2 \over {200}} + {{199} \over {200}}} \right]$$ = $${{201} \over 2}$$ = $$100{1 \over 2}$$
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