If the sum of $n$ terms of an $A.P.$ is $2n^2 + 5n$,then the $n^{th}$ term will be

Let ${a_1}, {a_2}, \dots, {a_{30}}$ be an $A.P.$,$S = \sum_{i=1}^{30} {a_i}$ and $T = \sum_{i=1}^{15} {a_{2i-1}}$. If ${a_5} = 27$ and $S - 2T = 75$,then ${a_{10}}$ is equal to:

If $\log_{3} 2, \log_{3} (2^{x} - 5)$ and $\log_{3} (2^{x} - \frac{7}{2})$ are in an Arithmetic Progression $(AP)$,then $x = \dots$

The $20^{\text{th}}$ term from the end of the progression $20, 19 \frac{1}{4}, 18 \frac{1}{2}, 17 \frac{3}{4}, \ldots, -129 \frac{1}{4}$ is:

$A$ 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 $T_m = 164$,then $m = $