Let $a _1, a _2, \ldots, a _{2024}$ be an Arithmetic Progression such that $a _1+\left( a _5+ a _{10}+ a _{15}+\ldots+ a _{2020}\right)+ a _{2024}= 2233$. Then $a_1+a_2+a_3+\ldots+a_{2024}$ is equal to ________

Consider a sequence whose sum of first $n$ -terms is given by $S_n = 4n^2 + 6n, n \in N$, then $T_{15}$ of this sequence is -

Three number are in $A.P.$ such that their sum is $18$ and sum of their squares is $158$. The greatest number among them is

Let ${a_1},{a_2},.......,{a_{30}}$ be an $A.P.$, $S = \sum\limits_{i = 1}^{30} {{a_i}} $ and $T = \sum\limits_{i = 1}^{15} {{a_{2i - 1}}} $.If ${a_5} = 27$ and $S - 2T = 75$ , then $a_{10}$ is equal to

If the ${n^{th}}$ term of an $A.P.$ be $(2n - 1)$, then the sum of its first $n$ terms will be

If $\left\{a_{i}\right\}_{i=1}^{n}$ where $n$ is an even integer, is an arithmetic progression with common difference $1$ , and $\sum \limits_{ i =1}^{ n } a _{ i }=192, \sum \limits_{ i =1}^{ n / 2} a _{2 i }=120$, then $n$ is equal to