Findanof {an} givena= 1, and1an+1 =Sn+ 2n+ 1

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- Mar 17th 2010, 07:08 PMMATNTRNGGeneral Term for a Sequence
Find

*a**n*of {*a**n*} given*a*= 1, and*1**a**n*+1 =*S**n*+ 2*n*+ 1 - Mar 17th 2010, 08:10 PMSoroban
Hello, MATNTRNG!

I hope the is a typo . . .

Quote:

Crank out the first few terms: .

Take the difference of consecutive terms,

. . then the differences of the differences, and so on.

. .

Since the*second*differences are constant,

. . the generating function is of the*second*degree, a quadratic.

The general quadratic function is: .

Use the first three values of the function and substitute:

. .

. .

. .

Substitute into [5]: .

Substitute into [3]: .

Therefore, the generating function is: .