If $p$ times the ${p^{th}}$ term of an $A.P.$ is equal to $q$ times the ${q^{th}}$ term of an $A.P.$, then ${(p + q)^{th}}$ term is
$0$
$1$
$2$
$3$
Different $A.P.$'s are constructed with the first term $100$,the last term $199$,And integral common differences. The sum of the common differences of all such, $A.P$'s having at least $3$ terms and at most $33$ terms is.
Let ${a_1},{a_2},{a_3}, \ldots $ be terms of $A.P.$ If $\frac{{{a_1} + {a_2} + \ldots + {a_p}}}{{{a_1} + {a_2} + \ldots + {a_q}}} = \frac{{{p^2}}}{{{q^2}}},p \ne q$ then $\frac{{{a_6}}}{{{a_{21}}}}$ equals
Which term of the sequence $( - 8 + 18i),\,( - 6 + 15i),$ $( - 4 + 12i)$ $,......$ is purely imaginary
If the sum and product of the first three term in an $A.P$. are $33$ and $1155$, respectively, then a value of its $11^{th}$ tern is
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 $11,$ then find the number of terms.