If the sum of the series $54 + 51 + 48 + .............$ is $513$, then the number of terms are
$18$
$20$
$17$
None of these
A series whose $n^{th}$ term is $\left( {\frac{n}{x}} \right) + y,$ the sum of $r$ terms will be
The difference between an integer and its cube is divisible by
${7^{th}}$ term of an $A.P.$ is $40$, then the sum of first $13$ terms is
If $1,\,\,{\log _9}({3^{1 - x}} + 2),\,\,{\log _3}({4.3^x} - 1)$ are in $A.P.$ then $x$ equals
Write the first five terms of the following sequence and obtain the corresponding series :
$a_{1}=3, a_{n}=3 a_{n-1}+2$ for all $n\,>\,1$