If the $7^{th}$ term of an Arithmetic Progression $(AP)$ is $40$,then the sum of its first $13$ terms is........

The sum of the first four terms of an arithmetic progression is $56$. The sum of the last four terms is $112$. If its first term is $11$, then the number of terms is:

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 the first term of an arithmetic progression is $a$,the common difference is $1$,and the last term is $b$,what is the sum of the progression?

Four numbers are in arithmetic progression. The sum of the first and last term is $8$ and the product of both middle terms is $15$. The least number of the series is

If three positive numbers $a, b,$ and $c$ are in $A.P.$ such that $abc = 8$,then the minimum possible value of $b$ is