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Mathematics · 2022 · 3 marks
CBSE 2022 · Region 4 · Set 3 · Q8
The sum of the first three terms of an A.P. is 33. If the product of first and third term exceeds the second term by 29, find the A.P.
The sum of the first three terms of an A.P. is 33. If the product of first and third term exceeds the second term by $\displaystyle 29$, find the A.P.
Marking-scheme solution
Let three terms of AP be \(\displaystyle a-d, a, a+d\)
\[\begin{aligned}
& \text { Sum }=33 \Rightarrow a-d+a+a+d=33 \\
& 3 a=33 \Rightarrow a=11
\end{aligned}
\]
When \(\displaystyle d=9, a=11\); A.P. is \(\displaystyle 2,11,20, \ldots\)
When \(\displaystyle d=-9, a=11\); A.P. is $\displaystyle 20$, $\displaystyle 11$, 2...
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