Lets say I have colony of 100 bacteria's.
Within 1 year, each of bacteria brings up a "child" and becomes "infertile".
After next year, children of bacteria bring up "children" and becomes "infertile".
Assuming that bacteria is immortal and will stay alive forever.
Which formula can I use for it in WolframAlpha?
I know sequence Plot [(formula), {a, start, end}, but how to form such formula in it?
For you it's walk in the park, that's because you're mathematicians. I am not.
In year $1$, there are $100$ bacteria.
In year $2$, there are $100+100$ bacteria.
In year $3$, there are $200+100$ bacteria.
etc.
Each year we get $100$ more bacteria. So in year $a$ there are $100\cdot a$ bacteria.
If your first year is year $0$, then your formula would be $100 \cdot(a+1)$.