The solution of the equation $(x + 1) + (x + 4) + (x + 7) + \dots + (x + 28) = 155$ is

The value of $\sum\limits_{r = 1}^n {\log \left( {\frac{{{a^r}}}{{{b^{r - 1}}}}} \right)} $ is

Let $T_r$ be the $r^{th}$ term of an $A.P.$ for $r = 1, 2, 3, \dots$. If for some positive integers $m, n$ we have $T_m = \frac{1}{n}$ and $T_n = \frac{1}{m}$,then $T_{mn}$ equals

Let $S_n$ denote the sum of the first $n$ terms of an $A.P$. If $S_4 = 16$ and $S_6 = -48$,then $S_{10}$ is equal to

If the $p^{th}$ term of an arithmetic progression is $q$ and the $q^{th}$ term is $p$,then its $n^{th}$ term is:

The first term of an $A.P.$ of consecutive integers is ${p^2} + 1$. The sum of $(2p + 1)$ terms of this series can be expressed as: