${7^{th}}$ term of an $A.P.$ is $40$, then the sum of first $13$ terms is
$53$
$520$
$1040$
$2080$
Insert $6$ numbers between $3$ and $24$ such that the resulting sequence is an $A.P.$
The sums of $n$ terms of two arithmetic progressions are in the ratio $5 n+4: 9 n+6 .$ Find the ratio of their $18^{\text {th }}$ terms.
If $a, b, c, d$ are in $G.P.,$ prove that $\left(a^{n}+b^{n}\right),\left(b^{n}+c^{n}\right),\left(c^{n}+d^{n}\right)$ are in $G.P.$
The number of terms common to the two A.P.'s $3,7,11, \ldots ., 407$ and $2,9,16, \ldots . .709$ is
If ${a^{1/x}} = {b^{1/y}} = {c^{1/z}}$ and $a,\;b,\;c$ are in $G.P.$, then $x,\;y,\;z$ will be in