If the sum of the $10$ terms of an $A.P.$ is $4$ times to the sum of its $5$ terms, then the ratio of first term and common difference is
$1:2$
$2:1$
$2:3$
$3:2$
The sum of all the elements of the set $\{\alpha \in\{1,2, \ldots, 100\}: \operatorname{HCF}(\alpha, 24)=1\}$ is
The sums of $n$ terms of two arithmatic series are in the ratio $2n + 3:6n + 5$, then the ratio of their ${13^{th}}$ terms is
Let ${S_n}$ denotes the sum of $n$ terms of an $A.P.$ If ${S_{2n}} = 3{S_n}$, then ratio $\frac{{{S_{3n}}}}{{{S_n}}} = $
Four numbers are in arithmetic progression. The sum of first and last term is $8$ and the product of both middle terms is $15$. The least number of the series is
If ${a^2},\;{b^2},\;{c^2}$ are in $A.P.$, then ${(b + c)^{ - 1}},\;{(c + a)^{ - 1}}$ and ${(a + b)^{ - 1}}$ will be in