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
The sums of $n$ terms of three $A.P.'s$ whose first term is $1$ and common differences are $1, 2, 3$ are ${S_1},\;{S_2},\;{S_3}$ respectively. The true relation is
If $a,b,c$ are in $A.P.$, then $\frac{1}{{\sqrt a + \sqrt b }},\,\frac{1}{{\sqrt a + \sqrt c }},$ $\frac{1}{{\sqrt b + \sqrt c }}$ are in
If the sum of a certain number of terms of the $A.P.$ $25,22,19, \ldots \ldots .$ is $116$ Find the last term
If the sum of the first $n$ terms of a series be $5{n^2} + 2n$, then its second term is
If the sides of a right angled traingle are in $A.P.$, then the sides are proportional to