different types of number series and their uses in real life What are the different types of number series that have practical uses in real life.
e.g. Fibonacci series, it is very important series which is present and useful in our nature. 
Please can you name any other series and their uses.
 A: Constant series is the most important of all: $a,a,a,...$ The reason is that everything continues in the same manner unless disturbed, and "the same manner" means something remaining constant by definition. Without this constant series, the world can only be in completely unpredictable chaotic chaos.
Linear series is the next most important: $a,a+b,a+2b,a+3b,...$ This is because the linear series is the only series with a constant change, and the constant series is the most important. In the physical world, many things have some properties that if allowed to remain constant will give rise to linear behaviour. For example, an object will have a constant velocity if nothing pushes or pulls it in any direction. It will also have a constant rate of rotation. Both of these mean that the position and orientation would be linear.
As you might expect, continuing this line of thought will yield polynomial series, that is $p(0),p(1),p(2),...$ where $p$ is a polynomial. Indeed the rate of change of position is velocity, the rate of change of velocity is acceleration, and the rate of change of acceleration is jerk. So integrating jerk gives acceleration, integrating again gives velocity, and integrating one more time gives position. In fact, polynomials can give good approximations to a lot of things, and natural extend to... power series, which isn't a series of the type you are looking for, but whatever.
Another common series in nature is the exponential series: $a,ar,ar^2,...$, which occur in plenty of things like population growth, dampening, decay, all these due to the fact that differential equations can be good approximators of relationships between quantities in even complicated systems.
A: Geometric is probably the big winner:
$$
c, ca, ca^2, ca^3, ca^4, \ldots
$$
represents growth of an account at interest rate $r$, compounded annually, where $c$ is the initial investment, and $a = 1+ r$. (Or growth of a bacterial culture in which there's an infinite supply of food, etc.)
Arthmetic:
$$
a, a + c, a + 2c, a + 3c, \ldots
$$
comes up for things growing at a constant rate. Used in very simple models of growth, where you say "we had $a$ units last year, and $a + c$ units this year, so maybe next year we'll have $a + 2c$." 
A: The Balmer series are useful for astronomy. It's one of six series describing the spectral line emissions of the hydrogen atom. It's calculated with the Balmer formula. See Wikipedia: Balmer series. Or for a list of all series: hydrogen spectral series.
