JEE Main 2013 (Online) 23rd AprilQuestion 1
If $a_1,a_2,a_3,\ldots,a_n,\ldots$ 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 :
Sequence and Series · Arithmetic Progression
Solution
Formulas used. (1) $a_p+a_q=2a_s$ when $p+q=2s$(2) $S_{13}=13\,a_7$ (middle term)Step 1 - Simplify. $4+10=2\times7$, so $a_4+a_{10}=2a_7$: $$a_4-a_7+a_{10}=2a_7-a_7=a_7=m .$$ Step 2. $$S_{13}=13\,a_7=13m .$$ Answer: (C)