Hi I need help with the following –
Do I need to use the geometric progression to work out the closed form?Consider the linear recurrence sequence:
x(subscript)1 = 5, x(subscript)n+1=1.2x(subscript)n-14 (n=1,2,3,…)
Find a closed form for the sequence.
Thanks.
Hello, mrszone!
It is not a geometric series . . . .Find the closed form: .
. .
Subtract [2] - [1]: .
Suppose the function is exponential: .
. . The equation becomes: .
. . which factors: .
. . and has nonzero roots: .
Form a linear combination of the two functions: .
From the first two values of the sequence:
. .
Subtract [4] - [3]: .
Substitute into [3]: .
Therefore: .
Edit: a silly typo! . . . fixed it.
.