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Mathematics · 2023 · 3 marks
CBSE 2023 · Region 5 · Set 3 · Q31
Find the common difference of an A.P. whose first term is 8, the last term is 65 and the sum of all its terms is 730.
Find the common difference of an A.P. whose first term is $\displaystyle 8$, the last term is $\displaystyle 65$ and the sum of all its terms is 730.
Marking-scheme solution
\[\begin{aligned}
& \mathrm{a}=8, l=65 \\
& 730=\frac{n}{2}[8+65] \\
& n=\frac{730 \times 2}{73}=20 \\
& \begin{aligned}
\therefore l=\mathrm{a}+19 \mathrm{~d} & \Rightarrow 65=18+19 \mathrm{~d} \\
& \Rightarrow \mathrm{~d}=3
\end{aligned}
\end{aligned}
\]
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