# Thread: Closed form for a sequence

1. ## Closed form for a sequence

i am having trouble with this sequence:

x1=3 xn+1=0.8 xn-5 (n=1,2,3....)

how do i find a closed form, also in the tenth term correct to 4SF

Can someone explain how can i describe a long term behaviour of the sequence

many thanks
rich

2. Originally Posted by scouse280
x1=3 xn+1=0.8 xn-5 (n=1,2,3....)
Please use the $\displaystyle math$ tag in order to make your equation readable. It is the third from right icon above the text editor and located next to the YouTube icon.

Best,
wirefree

3. Originally Posted by scouse280
i am having trouble with this sequence:

x1=3 xn+1=0.8 xn-5 (n=1,2,3....)

how do i find a closed form, also in the tenth term correct to 4SF

Can someone explain how can i describe a long term behaviour of the sequence

many thanks
rich
I take it that you mean $\displaystyle x_1= 3$ and $\displaystyle x_{n+1}= 0.8x_n- 5$. Notice that $\displaystyle x_2= 0.8x_1- 5$ and then $\displaystyle x_3= 0.8(0.8x_1- 5)- 5= x_1(0.8)^2- 5(0.8)- 5$, $\displaystyle x_4= 0.8((0.8)^2x_1- 5(0.8)- 5)- 5= x_1(0.8)^3- 5(0.8)^2- 5(0.8)- 5$