The number of terms common to the two A.P.'s $3,7,11, \ldots ., 407$ and $2,9,16, \ldots . .709$ is
$20$
$17$
$11$
$14$
When $9^{th}$ term of $A.P$ is divided by its $2^{nd}$ term then quotient is $5$ and when $13^{th}$ term is divided by $6^{th}$ term then quotient is $2$ and Remainder is $5$ then find first term of $A.P.$
If the ratio of the sum of $n$ terms of two $A.P.'s$ be $(7n + 1):(4n + 27)$, then the ratio of their ${11^{th}}$ terms will be
Let $S_n$ denote the sum of the first $n$ terms of an arithmetic progression. If $\mathrm{S}_{10}=390$ and the ratio of the tenth and the fifth terms is $15: 7$, then $S_{15}-S_5$ is equal to:
The interior angles of a polygon are in $A.P.$ If the smallest angle be ${120^o}$ and the common difference be $5^o$, then the number of sides is