They found a pattern in the successive terms and used it.
. . . .
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.
A2 = BA1 + C = BA + C ((1-B)/(1-B))
A3=...=(B^2)a + C((1-B^2)/(1-B))
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!
Yes you are right!
I didn't see the pattern, in every line the Ba+C is present and the only thing that changes is the power of B and the coefficient of C.
Unfortunately my reasoning was way more complicated including equations and roots in order to transform it to a geometric sequence which led me in nowhere!
It is a special sequence used in economy, and I guess it has its own characteristics and in order to make it geometric or arithmetic you would have to set B or C to special values (but then the general case is lost and and specific ones come up).
Thank you very very much, it was the piece I missed from the puzzle
I will keep in mind this pattern trick!!