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Mathematics · 2022 · 3 marks
CBSE 2022 · Region 4 · Set 2 · Q10
In an A.P., the sum of first n terms is n/2(3 n +5). Find the 25^th term of the A.P.
In an A.P., the sum of first n terms is $\displaystyle \frac{\mathrm{n}}{2}(3 \mathrm{n}+5)$. Find the $\displaystyle 25{ }^{\text {th }}$ term of the A.P.
Marking-scheme solution
\[\begin{aligned}
& S_{n}=\frac{3 n^{2}}{2}+\frac{5 n}{2} \\
& n=1, S_{1}=\frac{3}{2}+\frac{5}{2}=4 \rightarrow 1 \text { st term } a_{1} \\
& n=2, S_{2}=\frac{3 \times 4}{2}+\frac{5(2)}{2}=11(1 \text { st term }+ \text { 2nd term }) \\
& \therefore a_{2}=S_{2}-S_{1}=11-4=7 \\
& d=a_{2}-a_{1}=7-4=3 \\
& a_{25}=a+24 d=4+24(3)=76
\end{aligned}
\]
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CBSE Class 10 Mathematics past-paper question from the 2022 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.