MAT Exam 2025 Paper

Concept:An arithmetic series has terms written as $a+(n-1)d$, and its sum to $n$ terms is $S_n=\frac{n}{2}[2a+(n-1)d]$.Explanation:Let the first row have $a$ seats and the common difference be $d$.For the fifth row: $a+4d=22$.For the tenth row: $a+9d=37$.Subtracting the first equation from the second gives $(a+9d)-(a+4d)=37-22$.So, $5d=15$, which gives $d=3$.Substitute $d=3$ into $a+4d=22$: $a+12=22$, hence $a=10$.There are 26 rows, so $n=26$.Total seats $S_{26}=\frac{26}{2}[2(10)+(26-1)(3)]$.This simplifies to $13[20+75]=13\times 95=1,235$.Thus, the stadium has $1,235$ seats.Answer:The correct option is C. $1,235$ seats.