If the sum of $n$ terms of an $A$.$P$. is $3n^2 + 5n$ and its $m$th term is $164$, then the value of $m$ is

If $a$ and $b$ are two numbers,$A$ is the arithmetic mean,and $S$ is the sum of $n$ arithmetic means between $a$ and $b$,then what does $S/A$ depend on?

If $x, y, z$ are in an arithmetic progression,and $a$ is the arithmetic mean of $x$ and $y$,and $b$ is the arithmetic mean of $y$ and $z$,then what is the arithmetic mean of $a$ and $b$?

Find the sum of all natural numbers lying between $100$ and $1000$ which are multiples of $5.$

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?

The first term of an $A.P.$ is $2$ and the common difference is $4$. The sum of its $40$ terms will be: