If the sum of the series $54 + 51 + 48 + .............$ is $513$, then the number of terms are
$18$
$20$
$17$
None of these
If the ${p^{th}}$ term of an $A.P.$ be $q$ and ${q^{th}}$ term be $p$, then its ${r^{th}}$ term will be
The ratio of the sums of $m$ and $n$ terms of an $A.P.$ is $m^{2}: n^{2} .$ Show that the ratio of $m^{ th }$ and $n^{ th }$ term is $(2 m-1):(2 n-1)$
If the sum of three numbers of a arithmetic sequence is $15$ and the sum of their squares is $83$, then the numbers are
If $3^{2 \sin 2 \alpha-1},14$ and $3^{4-2 \sin 2 \alpha}$ are the first three terms of an $A.P.$ for some $\alpha$, then the sixth term of this $A.P.$ is
If $x,y,z$ are in $A.P. $ and ${\tan ^{ - 1}}x,{\tan ^{ - 1}}y$ and ${\tan ^{ - 1}}z$ are also in $A.P.$, then