Let T r be the r^(th) term of an A.P. If for some m, T m = 1/25, T₂₅ = 1/20, and 20 Σ r=1 ²⁵ T r = 13, then 5m Σ r=m ^(2m) T r is equal to

Sequence and Series: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q164

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumSequence and Series179× since 2002

Let

T_r

be the

r^{\text{th}}

term of an A.P. If for some

m

T_m = \frac{1}{25}

T_{25} = \frac{1}{20}

, and

20 \sum_{r=1}^{25} T_r = 13

, then

5m \sum_{r=m}^{2m} T_r

is equal to