The sum of the first four terms of an $A.P.$ is $56$. The sum of the last four terms is $112$. If its first term is $11$, the number of terms is
$10$
$11$
$12$
None of these
If the sum of three numbers in $A.P.,$ is $24$ and their product is $440,$ find the numbers.
If the sum of $\mathrm{n}$ terms of an $\mathrm{A.P.}$ is $n P+\frac{1}{2} n(n-1) Q,$ where $\mathrm{P}$ and $\mathrm{Q}$ are constants, find the common difference.
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
If ${m^{th}}$ terms of the series $63 + 65 + 67 + 69 + .........$ and $3 + 10 + 17 + 24 + ......$ be equal, then $m = $
If the variance of the terms in an increasing $A.P.$, $b _{1}, b _{2}, b _{3}, \ldots b _{11}$ is $90,$ then the common difference of this $A.P.$ is