QJEEM20Ma9d85: JEE Main 2020 Mathematics - Class 11 JEEM20Ma9d85 Solution: If the 10 th term of an A.P. is and its 20 th term is , then…

Question

Verified Solution • 2025–26 Session moderate

If the 10^th term of an A.P. is

{1 \over {20}}

and its 20^th term is

{1 \over {10}}

, then the sum of its first 200 terms is

Accepted Answer

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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