jee-main 2025 Q14

jee-main · India · session1_28jan_shift1 Arithmetic Sequences and Series Compute Partial Sum of an Arithmetic Sequence
Let $\mathrm { T } _ { \mathrm { r } }$ be the $\mathrm { r } ^ { \text {th} }$ term of an A.P. If for some $\mathrm { m } , T _ { m } = \frac { 1 } { 25 } , T _ { 25 } = \frac { 1 } { 20 }$, and $20 \sum _ { \mathrm { r } = 1 } ^ { 25 } T _ { \mathrm { r } } = 13$, then $5 \mathrm { m } \sum _ { \mathrm { r } = \mathrm { m } } ^ { 2 \mathrm { m } } T _ { \mathrm { r } }$ is equal to
(1) 98
(2) 126
(3) 142
(4) 112
Let $\mathrm { T } _ { \mathrm { r } }$ be the $\mathrm { r } ^ { \text {th} }$ term of an A.P. If for some $\mathrm { m } , T _ { m } = \frac { 1 } { 25 } , T _ { 25 } = \frac { 1 } { 20 }$, and $20 \sum _ { \mathrm { r } = 1 } ^ { 25 } T _ { \mathrm { r } } = 13$, then $5 \mathrm { m } \sum _ { \mathrm { r } = \mathrm { m } } ^ { 2 \mathrm { m } } T _ { \mathrm { r } }$ is equal to\\
(1) 98\\
(2) 126\\
(3) 142\\
(4) 112