Calculating the $100th$ term of a series I came across a series
$1,5,13,25,41,61.......$
I have to calculate the $100^{th}$ term of this series. How do I do it?
Is there any formula to calculate the $n^{th}$ term of a series?

The difference of successive terms forms an Arithmetic progression: $4,8,\cdots $. 
We can write the terms of our sequence as: $$0\times 4+1,1\times 4+1, 3\times 4+1, 6\times 4+1, 10\times 4+1, \cdots $$ $$=\frac {0\times 1}{2}\times 4+1, \frac {1\times 2}{2}\times 4+1, \frac {2\times 3}{2}\times 4+1, \frac {3\times 4}{2}\times 4+1, \cdots $$
We can see a pattern emerging. Thus the $n$th term of the sequence is $$\frac {n (n-1)}{2}\times 4+1 =4\binom {n}{2} +1$$ The hundredth term is thus $\boxed {4\binom {100}{2}+1=19801}$. Hope it helps. 
