Hello,

Given the sequence (An) with An+1 = BAn + C , A1=a, C not zero, B not 1

Find the formula (for general term) of this sequence.

Solution

A2 = BA1 + C = BA + C ((1-B)/(1-B))

A3=...=(B^2)a + C((1-B^2)/(1-B))

.... etc

it continues, then uses math induction etc and gives the solution that An = (B^n-1)M+N

I am not really asking for the result, my problem is very specific, is this:

((1-B)/(1-B))... which I don't understand where came from.

Thank you all!

Given the sequence (An) with An+1 = BAn + C , A1=a, C not zero, B not 1

Find the formula (for general term) of this sequence.

Solution

A2 = BA1 + C = BA + C ((1-B)/(1-B))

A3=...=(B^2)a + C((1-B^2)/(1-B))

.... etc

it continues, then uses math induction etc and gives the solution that An = (B^n-1)M+N

I am not really asking for the result, my problem is very specific, is this:

((1-B)/(1-B))... which I don't understand where came from.

Thank you all!

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