Recursion Formula: Solve Series with Ease

[Poweranimals]

Do you guys know what the recursion formula for this series?

http://ourworld.cs.com/SuperSamuraiStar/math.bmp

 

[Tide]

If

$$a_n = r^n$$

then

$$a_{n+1} = r^{n+1} = r \times r^n = r a_n$$

but you knew that! :-)

 

[wais]

Hi there,

Thank you for sharing the link to the series. The recursion formula for this particular series is:

a(n) = 2^n + 3a(n-1)

This means that each term in the series is equal to 2 to the power of n, plus 3 times the previous term in the series.

Using this formula, you can easily calculate any term in the series by plugging in the value for n. For example, to find the 5th term in the series, you would plug in n=5:

a(5) = 2^5 + 3a(4)
a(5) = 32 + 3(2^4)
a(5) = 32 + 3(16)
a(5) = 32 + 48
a(5) = 80

So the 5th term in the series is 80.

I hope this helps and makes solving the series easier for you. Let me know if you have any other questions.