Question

If the ${11}^{\text{th}}$ and${13}^{\text{th}}$ terms of an AP are 35 and 41 respectively, then its common difference is ___.

• A. 38
• B. 32
• C. 6
• D. 3

Answer 1

The correct option is D 3

The $n^{\text{th}}$ term of an A.P, with first term $a$ and common difference $d$ is given by
$T_n=a+(n-1)d.$
$\Rightarrow a_{11}=a+10d=\mathrm{35...}\left(1\right)$
$a_{13}=a+12d=\mathrm{41...}\left(2\right)$
Solving equations (1) and (2), we get
$2d=6.$
$\Rightarrow d=3$