The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be
A. 5 B. 6 C. 7 D. 8 Answer: Option BShow Answer
Solution(By Apex Team)
First term of an A.P. (a) = 1
Last term (l) = 11
and sum of its terms = 36
Let n be the number of terms and d be the common difference, then
$\begin{aligned}&a_n=1=a+(n-1)d=11\\
&\Rightarrow1+(n-1)d=11\\
&\Rightarrow(n-1)d=11-1\\
&\Rightarrow(n-1)d=10\ldots\\
&S_n=\frac{n}{2}[2a+(n-1)d]=36\\
&\Rightarrow\frac{n}{2}[2\times1+10]=36\quad[\text{ From }(1)]\\
&\Rightarrow n(2+10)=72\\
&\Rightarrow12n=72\\
&\Rightarrow n=\frac{72}{12}\\
&\Rightarrow n=6\end{aligned}$
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