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Mathematics · 2022 · 2 marks
CBSE 2022 · Region 2 · Set 3 · Q3
(a) In an A.P. if the sum of third and seventh term is zero, find its 5^th term.
(a)
In an A.P. if the sum of third and seventh term is zero, find its $\displaystyle \mathbf{5}^{\text {th }}$ term.
OR
(b)
Determine the A.P. whose third term is $\displaystyle 5$ and seventh term is 9.
Marking-scheme solution
\[\begin{aligned}
& (a+2 d)+(a+6 d)=0 \\
& \Rightarrow a=-4 d
\end{aligned}
\]
Hence \(\displaystyle a_{5}=0\)
Or
\[a+2 d=5, a+6 d=9
\]
\[\Rightarrow a=3, d=1
\]
Therefore A.P. is \(\displaystyle 3,4,5, \ldots\)
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