The sums of $n$ terms of two arithmetic series are in the ratio $(2n + 3) : (6n + 5)$. Then the ratio of their $13^{th}$ terms is:

$A$ farmer buys a used tractor for $Rs. 12000$. He pays $Rs. 6000$ cash and agrees to pay the balance in annual instalments of $Rs. 500$ plus $12\%$ interest on the unpaid amount. How much will the tractor cost him?

Five numbers are in $A.P.$,whose sum is $25$ and product is $2520$. If one of these five numbers is $-\frac{1}{2}$,then the greatest number amongst them is

Let $s_1, s_2, s_3, \ldots, s_{10}$ be the sum of the first $12$ terms of $10$ arithmetic progressions whose first terms are $1, 2, 3, \ldots, 10$ and whose common differences are $1, 3, 5, \ldots, 19$ respectively. Then $\sum_{i=1}^{10} s_i$ is equal to

If the $p^{th}$ term of an arithmetic progression is $q$ and the $q^{th}$ term is $p$,then its $r^{th}$ term is:

After inserting $n$ arithmetic means $(A.M.s)$ between $2$ and $38$,the sum of the resulting progression is $200$. The value of $n$ is