jee-main 2022 Q63

jee-main · India · session1_24jun_shift1 Arithmetic Sequences and Series Counting or Combinatorial Problems on APs
If $\left\{ a _ { i } \right\} _ { i = 1 } ^ { \mathrm { n } }$, where $n$ is an even integer, is an arithmetic progression with common difference 1 , and $\sum _ { i = 1 } ^ { n } a _ { i } = 192 , \sum _ { i = 1 } ^ { \frac { n } { 2 } } a _ { 2 i } = 120$, then $n$ is equal to
(1) 18
(2) 36
(3) 96
(4) 48
If $\left\{ a _ { i } \right\} _ { i = 1 } ^ { \mathrm { n } }$, where $n$ is an even integer, is an arithmetic progression with common difference 1 , and $\sum _ { i = 1 } ^ { n } a _ { i } = 192 , \sum _ { i = 1 } ^ { \frac { n } { 2 } } a _ { 2 i } = 120$, then $n$ is equal to\\
(1) 18\\
(2) 36\\
(3) 96\\
(4) 48