Question:
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
Solution:
(b) 6
$a=1, a_{n}=11, S_{n}=36$
$\because a_{n}=11$
$\Rightarrow a+(n-1) d=11$
$\Rightarrow 1+(n-1) d=11$
$\Rightarrow(n-1) d=10$ ....(1)
Also, $S_{n}=36$
$\Rightarrow \frac{n}{2}\{2 a+(n-1) d\}=36$
$\Rightarrow n\{2+10\}=72$ (Using (1))
$\Rightarrow n=6$