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Mathematics · 2026 · 2 marks
CBSE 2026 · Region 3 · Set 1 · Q22
In an A.P., the first term is $\displaystyle 32$ and the last term is - 10. If the common difference is -$\displaystyle 2$, then find the number of terms and their sum.Find the sum of the first $\displaystyle 28$ terms of an A.P. whose $\displaystyle \mathrm{n}^{\text {th }}$ term is given by $\displaystyle \mathrm{a}_{\mathrm{n}}=3 \mathrm{n}-2$.
In an A.P., the first term is $\displaystyle 32$ and the last term is - 10. If the common difference is -$\displaystyle 2$, then find the number of terms and their sum.
Find the sum of the first $\displaystyle 28$ terms of an A.P. whose $\displaystyle \mathrm{n}^{\text {th }}$ term is given by $\displaystyle \mathrm{a}_{\mathrm{n}}=3 \mathrm{n}-2$.
Marking-scheme solution
Here \(\displaystyle \mathrm{a}=32, l=-10\) and \(\displaystyle \mathrm{d}=-2\)
\[\begin{aligned}
& \therefore 32+(\mathrm{n}-1)(-2)=- \\
& \Rightarrow \mathrm{n}=22 \\
& \mathrm{~S}_{22}=\frac{22}{2} \times[32+(-10)] \\
& \quad=242
\end{aligned}
\]
\[\begin{aligned}
& \mathrm{a}_{1}=3(1)-2=1 \\
& \text { and } \mathrm{a}_{28}=3(28)-2=82 \\
& \begin{aligned}
\mathrm{S}_{28} & =\frac{28}{2} \times(1+82) \\
& =1162
\end{aligned}
\end{aligned}
\]
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CBSE Class 10 Mathematics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.