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
$A.P.$
$G.P.$
$H.P.$
None of these
The four arithmetic means between $3$ and $23$ are
Write the first five terms of the sequences whose $n^{t h}$ term is $a_{n}=n(n+2)$
The sum of the first and third term of an arithmetic progression is $12$ and the product of first and second term is $24$, then first term is
Find the sum of integers from $1$ to $100$ that are divisible by $2$ or $5.$
The sides of a triangle are distinct positive integers in an arithmetic progression. If the smallest side is $10$, the number of such triangles is