[Discrete Mathematics] Homogeneous Recurrence Relations Examples

We do two examples with homogeneous recurrence relations.
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[@jawdatkour536]

I am very grateful to you for your effort,
I have one question please , I just need to check what the recurrence relation is in this
example:
A particle moves horizontally to the right. For n belongs Z+, the distance
the particle travels in the (n + 1)st second is equal to 4 times the distance
it travels during the nth second. If x_n; n 0, denotes the position of the
particle at the start of the (n+1)st second, find a recurrence relation for x_n,
where x0 = 1 and x1 = 3. Solve it on the computer. Plot with command
DiscretePlot the first 10 values of x_n (and logarithm for higher values).
thank you ,

[@1Eagler]

Jawdat Kour An+1= 3*4^n

[@jaehoonyi2]

Thanks for this. Best illustration/teaching of Discrete math anywhere online. You should teach our class. Also, I think there was a misunderstanding at 7:04 with moving the '9' to the other side. Correct me if i'm wrong. Thanks again.

[@SmartPieBoy99]

I think its because a1=-3 so when he was bringing the 9 over he took three from it. That got me too

[@oromiastar]

awesome
👌👌👌

[@Khadari2013]

thanks man that was great!!

[@somethingelles]

How did you come up with the new matrix from the original matrix? Can someone please explain

[@user-yq6lf9le4k]

The first exercise there seems to be a great problem because the formula consistently doesn't work for a⁰ but works for everything else

[@mohammadrezajavadi3498]

Fantastic

[@harendrasingh_22]

Awesome. Thanks

[@samueldarko9360]

How did u factorise to get 3 and -2. I get surd answers

[@JonathanPeel]

At around 6:08.
How does n become negative, if (n+3)^2=0 ?

[@alexsayshi6782]

n+3 = 0; so then subtract 3 both sides, and n = -3

[@JonathanPeel]

@@alexsayshi6782 thank you the time you took to reply to me.
I just rewatched, and I don't know what headspace I was in to not see that the first time 😵‍💫
I do get it. 👍🏻