**WELL I DID !!**

**Have you ever been in math class and wondered ... when will I ever use math in real life?**

A geometric sequence/series in real life

When you think about basketball being a real life example of arithmetic sequences and series, you probably start to think .. Well how could we make a basketball game into an explicit or recursive formula? Easy :) !

Now, if you wanted to find out how many parents there will be 10 generations later, when only starting off with one set of parents, you could use the recursive and/or explicit formulas below.

Every family starts off with a mom and dad. From there, the mom and dad have children. Those children in turn, then have there own kids. Those kids have more. So on and so on .. right? You would get a sequence that looks something like - 1, 2, 4, 8, 16 and so on.

I know a lot of you probably watch or have watched basketball before. But I can almost bet on it that you haven't thought of it as an example of an arithmetic sequences and series. When you think about it, the object of the game is to score the most point, right? But, the amount of points you can get from a normal shoot is 2 points ... right? Well then, from that couldn't you get a geometric sequence. Something like 2, 4, 6, 8, 10 and so on.

An arithmetic sequence/series in real life

Let's say you wanted to figure out what the score will be after the Miami Heats make 87 shots.

You could use the recursive formula of

You could also use the explicit formula of

+2

2

2

Which ever formula you decide to use, you should get the same answer of 174. Telling you that, in this basketball game, if the Miami Heats make 87 (two-point shots) they would have scored a total of 174 points. Not bad :) !

To sum them all up you could also use the summation notation of

87

2)

**Thank you**

Now, just as easily as it is to find an arithmetic sequence/series in real life, you can find a geometric sequence/series. Its as simple as thinking of a family reproducing and keeping the family name around.

I don't know about you, but I know sometimes people wonder about their ancestors or how about wondering, "Hmm, how many other people have that last name because of their family roots?" . Something as simple as that can make someone use some math in that moment to figure out the answer to that.

The recursive formula would be :

The explicit formula would be :

2

2

For which ever formula you use, you should get the answer of 512 .

You could also use the summation notation of

10

1

( 1-2 )

( 1-2 )

10

-Pranav Chheda