Math problem.

[Tyjet66]

I want to start with X, divided by 2, and add that number back to X to create Y.

That alone is easy. Y=X/2+X

I specifically want to start with 8=X. So Y=12, 18, 27....

Here is my problem, I want to repeat the original equation 8,000 times to create a larger and larger number. Short of doing that equation by hand 8,000 times, how would I go about doing this?

I really hope there isn't a simple answer that I'm somehow not seeing. Thanks for your time.

 

[Sa967St]

Re-write the equation as y=1.5x.

What do you mean you want to repeat it 8000 times? Do you just want the 8000th y term, or do you want all y terms from the 1st-8000th?

 

[Tyjet66]

Yes, the 8000th y term. Thanks for your help.

 

[Sa967St]

The recursive equation is t(n)=1.5*t(n-1) where t(0)=12.
Find the non-recursive equation in terms of x and y for generating {12, 18, 27, 41.25, 61.875 ...}, then you can plug in x=8000.

 

[Meep]

If you start writing out the first few,

1: 12
2: 12*1.5 = 18
3: 18*1.5 = 27

You can notice that it can also be written like

1: 12
2: 12*1.5 = 18
3: 12*1.5*1.5 = 27

or

1: 12*(1.5)^0
2: 12*(1.5)^1
3: 12*(1.5)^2

So from that it should be clear that the nth term (Where 12 is the 1st) is 12*(1.5)^(n-1)

 

[immortalchaos29]

Just typed this into C++

int main()

double y=0
double x=8
for int(i=0; i<8000; i++)

y = 1.5*x;
x = y;

and it returned the value "infinity" lol

if you use i<1725 it returns 4.57627*10^304
So you can imagine how high it must be for i = 8000 O.O

Like you said... not sure if there's an easier way.

 

[tozies24]

Why do you need it for the 8000th term?

 

[Tyjet66]

I appreciate the help everyone. I now know the number is just too massive to comprehend lol. Someone had posed a question to me of a topic relating to this equation, I can't quite remember how the 8000th term came up but I was curious. A lot of my math class knowledge has kinda faded away, as much as I hate to say it.

 

[nitay6669]

i think wolfram alpha will be able to solve this, but getting the input right is tricky.
he once solved for me 2008!

 

[whauk]

wolfram alpha easily solves this:
http://www.wolframalpha.com/input/?i=8*1.5^8000
seems to be 4.3*10^1409

 

[peterbone]

Even windows calculator solves this. Gives the same answer.