Question

solve the difference equation yn+1=-.8Yn+90

Answer 1

got any answers to this

Answer 2

yn=111.25 if wrong correct me

Answer 3

forget yn+1

Answer 4

just 1=-0.8yn+90

Answer 5

do opposite of add its subtract

Answer 6

so 1-90=-89

Answer 7

-89/-0.8=111.25

Answer 8

\[\begin{align}y_{n+1} &= -0.8Y_n +90\\~\\&=-0.8\left(-0.8Y_{n-1} + 90\right) + 90 = (-0.8)^2Y_{n-1} + 90(1 -0.8)\\~\\&=(-0.8)^2(-0.8Y_{n-2}+90) + 90(1 -0.8) = (-0.8)^3Y_{n-2} + 90(1 -0.8 + (-0.8)^2)\\~\\~\\&=\end{align}\]

Answer 9

see any pattern ?

Answer 10

omg, i figured it out! thank you!

Answer 11

contunuing further you would get :
\[\large Y_{n+1} = (-0.8)^{n}Y_1 + 90\left(\dfrac{1-(-0.8)^{n}}{1-(-0.8)}\right) \]

Answer 12

right