Which term of the sequence $(-8 + 18i), (-6 + 15i), (-4 + 12i), \dots$ is purely imaginary (in $^{th}$)?

The common difference of the $A.P.: a_{1}, a_{2}, ..., a_{m}$ is $13$ more than the common difference of the $A.P.: b_{1}, b_{2}, ..., b_{n}$. If $b_{31} = -277$,$b_{43} = -385$ and $a_{78} = 327$,then $a_{1}$ is equal to

Write the first five terms of the sequence whose $n^{th}$ term is $a_{n} = \frac{2n - 3}{6}$.

Three numbers are in $A.P.$ whose sum is $33$ and product is $792$. The smallest number among these is:

If the sum of the first four terms of an $A.P.$ is $6$ and the sum of its first six terms is $4$,then the sum of its first twelve terms is

The ${n^{th}}$ term of the series $3 \cdot 8 + 6 \cdot 11 + 9 \cdot 14 + 12 \cdot 17 + \dots$ will be