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JEE Main 29-Jan-2025 Paper - Shift 2 — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEEJEE Main 29-Jan-2025 Paper - Shift 24 Marks
Question
Let $a_1, a_2, \ldots, a_{204}$ be an Arithmetic Progression such that $a _1+\left( a _5+ a _{10}+ a _{19}+\ldots+ a _{2000}\right)+ a _{2254}=$ 2233. Then $a_1+a_2+a_3+\ldots+a_{3034}$ is equal to _________
✓

Answer

(11132)
Sol. $a_1+a_5+a_{10}+\ldots \ldots+a_{2000}+a_{2024}=2233$
In an A.P. the sum of terms equidistant from ends is equal.$
\begin{array}{l}
a_1+a_{204}=a_5+a_{3000}=a_{10}+a_{2015} \ldots \ldots \\
\Rightarrow 203 \text { pairs } \\
\Rightarrow 203\left(a_1+a_{304}\right)=2233
\end{array}
$
Hence,
$
\begin{array}{l}
S_{2124}=\frac{2024}{2}\left(a_1+a_{2024}\right) \\
=1012 \times 11 \\
=11132
\end{array}
$

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