The sums of $n$ terms of two arithmatic series are in the ratio $2n + 3:6n + 5$, then the ratio of their ${13^{th}}$ terms is
$53 : 155$
$27 : 77$
$29 : 83$
$31 : 89$
What is the sum of all two digit numbers which give a remainder of $4$ when divided by $6$ ?
The mean of the series $a,a + nd,\,\,a + 2nd$ is
The sum of $n$ terms of two arithmetic progressions are in the ratio $(3 n+8):(7 n+15) .$ Find the ratio of their $12^{\text {th }}$ terms.
The value of $\sum\limits_{r = 1}^n {\log \left( {\frac{{{a^r}}}{{{b^{r - 1}}}}} \right)} $ is