Question

If $a_1,a_2,a_3,..,a_n,..$ are in $A.P$. Such that $a_4-a_7+a_{10}=m,$ then the sum of first $13$ terms of this $A.P$., is :

• A. $15m$
• B. $10m$
• C. $12m$
• D. $13m$

Answer 1

Answer: (D)

$13m$

$a_4-a_7+a_{10}=m$

$\Rightarrow \left(a+3d\right)-\left(a+6d\right)+a+9d=m$

$\Rightarrow a+3d-a-6d+a+9d=m$

$\Rightarrow 6d+a=m\left(1\right)$

$S_{13}=\frac{13}{2}\left(2a+\left(13-1\right)d\right)$

$=\frac{13}{2}\left(2a+12d\right)$

$=13\left(a+6d\right)$

$=13m$