Help with a Sequence

[digitalmaster287]

Does anyone know if there are any real world applications to a sequence where each number is equal to the preceding number multiplied by something and then added to something?

Like, for example:

1, 3, 11, 43...

In the above, each number is multiplied by 4 and then subtracted by 1 to get the next number

4, 6, 10, 18

In that one, each number is multiplied by 2 and then subtracted by 2

Also, are there any real world applications for the sum of this sequence?

I was just wondering this because I have to write a paper in Math where I could pick the topic and I need to find out an application of this sequence if I am to do my paper on it. I already have the proof for the nth term and the sum of this worked out, it's just that I need to find something that it would be useful for.

 

[Johnthegalactic]

I dont know, but I think it was trig functions or something, that I noticed they would be useful in Naval gunnery for range finding.
Where it is that you have the height of yourself(height of ship), angle at which the object you see is floating, and your angle from the water(90deg, give take a few due to movement), then you find the distance to the ship using some math stuff, anyway.
In short, you use math to figure out how high to point your guns so the shells slam into the ship, although, nowadays, we don't use battleships anymore.

 

[digitalmaster287]

I dont know, but I think it was trig functions or something, that I noticed they would be useful in Naval gunnery for range finding.
Where it is that you have the height of yourself(height of ship), angle at which the object you see is floating, and your angle from the water(90deg, give take a few due to movement), then you find the distance to the ship using some math stuff, anyway.
In short, you use math to figure out how high to point your guns so the shells slam into the ship, although, nowadays, we don't use battleships anymore.

Can you explain what that has to do with that sequence, because it just seems like trigonometry to me.