Mathematics - Sequence & Series Question with Solution | TestHub

As $a_1+a_5+a_{10}+\dots +a_{2020}+a_{2024}=2233$ ...(1) We know in arithmetic progression. Sum of terms equidistant from ends is equal $\therefore$ from (1) $\underset{203\text{ pairs }}{\underbrace{a_1+a_{2024}=a_5+a_{2020}=a_{10}+a_{2015}=\dots }}$ $\begin{array}{rl}& \Rightarrow 203\left(a_1+a_{2024}\right)=2233\\ & \Rightarrow a_1+a_{2024}=11\end{array}$ Now $\begin{array}{rl}\sum _{i=1}^{2024}{a}_i& =S_{2024}=\frac{2024}{2}\left[a_1+a_{2024}\right]\\ & =1012(11)\\ & =11132\end{array}$