Could anyone direct me on how to solve these? Im stuck. (n-1 are subscripts)

An=2An-1 -3, a0 = -1

An=(n+1)An-1, a0=2

An=2nAn-1, a0=3

An=-An-1 + n - 1, a0 = 7

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- March 22nd 2009, 08:18 AMvexikedRecurrence Relation
Could anyone direct me on how to solve these? Im stuck. (n-1 are subscripts)

An=2An-1 -3, a0 = -1

An=(n+1)An-1, a0=2

An=2nAn-1, a0=3

An=-An-1 + n - 1, a0 = 7

- March 22nd 2009, 09:21 AMvexiked
Even a general method would help! Thanks

- March 22nd 2009, 10:46 AMSoroban
Hello, vexiked!

I'll walk through the first one.

Quote:

Could anyone direct me on how to solve these?

We conjecture that is of the form: . , an exponential expression.

Subtract [2] - [1]: .

Divide by

. . Hence, the function has: .

Form a linear combination of the two roots: .

. . and we have: .

Use the first two terms of the sequence:

. .

Subtract [4] - [3]: .

Substitute into [3]: .

Therefore: .