The sum of the series $1 + 3 + 5 + 7 + \dots$ up to $n$ terms is equal to:

Let $\sum_{k=1}^{n} a_{k} = \alpha n^{2} + \beta n$. If $a_{10} = 59$ and $a_{6} = 7a_{1}$,then $\alpha + \beta$ is equal to:

If $2x, x + 8$ and $3x + 1$ are in an arithmetic progression,then $x = \dots$

$A$ man deposited $Rs. 10000$ in a bank at the rate of $5\%$ simple interest annually. Find the amount in the $15^{\text{th}}$ year since he deposited the amount and also calculate the total amount after $20$ years.

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 the first term of an $A.P.$ is $3$ and the sum of its first four terms is equal to one-fifth of the sum of the next four terms,then the sum of the first $20$ terms is equal to