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
If $\frac{a}{b},\frac{b}{c},\frac{c}{a}$ are in $H.P.$, then
Write the first five terms of the sequences whose $n^{t h}$ term is $a_{n}=(-1)^{n-1} 5^{n+1}$
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
Let $3,7,11,15, \ldots, 403$ and $2,5,8,11, \ldots, 404$ be two arithmetic progressions. Then the sum, of the common terms in them, is equal to.....................