Let $a_1=8, a_2, a_3, \ldots, a_n$ be an $A.P.$ If the sum of its first four terms is $50$ and the sum of its last four terms is $170$,then the product of its middle two terms is

Given an $A.P.$ whose terms are all positive integers. The sum of its first nine terms is greater than $200$ and less than $220$. If the second term is $12$,then its $4^{th}$ term is:

Find the $25^{th}$ common term of the following $A.P.'s$:
$S_1 = 1, 6, 11, .....$
$S_2 = 3, 7, 11, .....$

Let $a_1, a_2, a_3, \ldots$ be in an $A.P.$ such that $\sum_{k=1}^{12} a_{2k-1} = -\frac{72}{5} a_1$,where $a_1 \neq 0$. If $\sum_{k=1}^{n} a_k = 0$,then $n$ is:

Shamshad Ali buys a scooter for $Rs. 22000$. He pays $Rs. 4000$ cash and agrees to pay the balance in annual installments of $Rs. 1000$ plus $10\%$ interest on the unpaid amount. How much will the scooter cost him in total?

If the sum of the first $21$ terms of the series $\log _{9^{1 / 2}} x + \log _{9^{1 / 3}} x + \log _{9^{1 / 4}} x + \dots$ where $x > 0$ is $504$,then $x$ is equal to: