KEAM 2013 Math Paper

Let a and d be the first term and common difference, respectively.
Given, ‌‌T2=13⇒a+d=13....(i)
According to the question,
(add‌a1+a2+...+a10 on both sides )
⇒‌‌6a+27d=4a+38d
⇒‌‌2a=11d....(ii)
From Eqs. (i) and (ii), we get