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

Answer 1

The correct option is B

6

$a=1,a_n=11,S_n=36$

$\because a_n=11$

$\Rightarrow a+(n-1)d=11$

$\Rightarrow 1+(n-1)d=11$

$\Rightarrow (n-1)d=10$

Also, $S_n=36$

$\Rightarrow \frac{n}{2}\{2a+(n-1\left)d\right\}=36$

$\Rightarrow n\{2+10\}=72$ [Using (1)]

$\Rightarrow n=6$