This DE has characteristic equation

with a repeated root at r = 3/2. Then the characteristic solution is

which has derivative

Use the given initial conditions to solve for the constants:


and so the particular solution to the IVP is

So basically the height is divided by a certain number to evenly divide it
Do you mean a_(n+1), worded a sub (n+1)?
If so yes. If the function of the sequence is getting smaller or more negative with each term.
The answer is 12 good luck;)