Suppose that all the terms of an arithmetic progression ($A.P.$) are natural numbers. If the ratio of the sum of the first seven terms to the sum of the first eleven terms is $6: 11$ and the seventh term lies in between $130$ and $140$ , then the common difference of this $A.P.$ is
$6$
$7$
$8$
$9$
If $\frac{{3 + 5 + 7 + ..........{\rm{to}}\;n\;{\rm{terms}}}}{{5 + 8 + 11 + .........{\rm{to}}\;10\;{\rm{terms}}}} = 7$, then the value of $n$ is
Find the $20^{\text {th }}$ term in the following sequence whose $n^{\text {th }}$ term is $a_{n}=\frac{n(n-2)}{n+3}$
If $(b+c),(c+a),(a+b)$ are in $H.P$ , then $a^2,b^2,c^2$ are in.......
In $\Delta ABC$, if $a, b, c$ are in $A.P.$ (with usual notations), identify the incorrect statements -
If the angles of a quadrilateral are in $A.P.$ whose common difference is ${10^o}$, then the angles of the quadrilateral are