For an $A.P.$,the first term is $10$ and the $10^{th}$ term is $100$. Then,the sum of the first $10$ terms is..........

The sums of $n$ terms,$2n$ terms,and $3n$ terms of an $A.P.$ are $S_1, S_2,$ and $S_3$ respectively. Prove that $S_3 = 3(S_2 - S_1)$.

$A$ plastic toy consists of $14$ circular discs of different radii. The radius of the smallest disc is $1\, cm$, the radius of the next bigger disc is $2\, cm$, and so on, such that the radius of the biggest disc is $14\, cm$. Find the sum of the circumferences of all the discs in $cm$.

Find the sum of the multiples of $3$ lying between $250$ and $1000$.

In an $AP$,if $a = 1$,$a_{n} = 20$,and $S_{n} = 399$,then $n$ is:

Find the sum of the first $24$ terms of the list of numbers whose $n^{th}$ term is given by $a_{n} = 3 + 2n$.