I am not able to implement the solution

#1

in the hint video it was stated that the first element of f1 vector is Sn but how will i able to get Sn to calculate Sn+1
rest part is understandable but can you just write code of how to calculate f1 vector some of solutions i have put f1[1]=0 which i am unable to understand so please provide code for f1 vector or a screen shot explaining the how the elements are inserted;

#2

and in seq the f1 vector is nothing but the first k terms of the sequence which is vector b1 but for Sn+1 how to we derive the f1 vector

#3

here is the code for your reference

#4

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