If the ratio of the sum of $n$ terms of two arithmetic progressions is $(7n + 1) : (4n + 27)$,then what is the ratio of their $11^{th}$ terms?

Six numbers are in an $AP$ such that their sum is $3$. The first term is $4$ times the third term. Then,the fifth term is:

Three positive numbers $a, b,$ and $c$ are in an Arithmetic Progression $(AP)$ and $abc = 4$. The minimum possible value of $b$ is:

The houses on one side of a road are numbered using consecutive even numbers. The sum of the numbers of all the houses in that row is $170$. If there are at least $6$ houses in that row and $a$ is the number of the sixth house,then:

If $100$ times the $100^{th}$ term of an Arithmetic Progression with a non-zero common difference is equal to $50$ times its $50^{th}$ term,then what is its $150^{th}$ term?

If $a_r > 0, r \in N$ and $a_1, a_2, a_3, ..., a_{2n}$ are in an arithmetic progression,then $\frac{a_1 + a_{2n}}{\sqrt{a_1} + \sqrt{a_2}} + \frac{a_2 + a_{2n-1}}{\sqrt{a_2} + \sqrt{a_3}} + \frac{a_3 + a_{2n-2}}{\sqrt{a_3} + \sqrt{a_4}} + ... + \frac{a_n + a_{n+1}}{\sqrt{a_n} + \sqrt{a_{n+1}}} = ?$