If the sum of three numbers of a arithmetic sequence is $15$ and the sum of their squares is $83$, then the numbers are
$4, 5, 6$
$3, 5, 7$
$1, 5, 9$
$2, 5, 8$
If $19^{th}$ terms of non -zero $A.P.$ is zero, then its ($49^{th}$ term) : ($29^{th}$ term) is
If ${S_n} = nP + \frac{1}{2}n(n - 1)Q$, where ${S_n}$ denotes the sum of the first $n$ terms of an $A.P.$, then the common difference is
If $b + c,$ $c + a,$ $a + b$ are in $H.P.$, then $\frac{a}{{b + c}},\frac{b}{{c + a}},\frac{c}{{a + b}}$ are in
The sum of the integers from $1$ to $100$ which are not divisible by $3$ or $5$ is
Suppose that all the terms of an arithmetic progression ($A.P.$) are natural numbers. If the ratio of the sum of the first seven terms to the sum of the first eleven terms is $6: 11$ and the seventh term lies in between $130$ and $140$ , then the common difference of this $A.P.$ is