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. 10 m
• B. 12 m
• C. 13 m
• D. 15 m

Answer 1

Answer: (C)

If $d$ be the common difference, then
$m=a_{4}-a_{7}+a_{10}=a_{4}-a_{7}+a_{7}+3d=a_{7}$
$S_{13}=\frac{13}{2}\left[a_{1}+a_{13}\right]=\frac{13}{2}\left[a_{1}+a_{7}+6d\right]$
$=\frac{13}{2}\left[2a_{7}\right]=13a_{7}=13\,m$