Frontend JS Algorithms If we are presented with the first

k terms of a sequence it is impossible to say with certainty the
value of the next term, as there are infinitely many polynomial functions that can model the
sequence.
As an example, let us consider the sequence of cube numbers. This is defined by the generating
function,
un = n3
: 1, 8, 27, 64, 125, 216, ...
Suppose we were only given the first two terms of this sequence. Working on the principle that
"simple is best" we should assume a linear relationship and predict the next term to be 15 (common
difference 7). Even if we were presented with the first three terms, by the same principle of
simplicity, a quadratic relationship should be assumed. We shall define OP (k, n) to be the nth term
of the optimum polynomial generating function for the first k terms of a sequence. It should be
clear that OP (k, n) will accurately generate the terms of the sequence for n ≤ k, and potentially
the first incorrect term (FIT) will be OP (k, k + 1); in which case we shall call it a bad OP (BOP) .As
a basis, if we were only given the first term of sequence, it would be most sensible to assume
constancy; that is, for n ≥ 2, OP (1, n) = u1.
Hence we obtain the following OPs for the cubic sequence:
OP (1, n) = 1
1, 1, 1, 1, ...
OP (2, n) = 7n − 6
1, 8, 15, ...
OP (3, n) = 6n2
−11n + 6
1, 8, 27, 58, ...
OP (4, n) = n3
1, 8, 27, 64, 125, ...
Clearly no BOPs exist for k ≥ 4.
By considering the sum of FITs generated by the BOPs (indicated in red above), we obtain 1 + 15
+ 58 = 74.
Consider the following tenth degree polynomial generating function:
un = 1 - n + n2 - n3 + n4 - n5 + n6 - n7 + n8 - n9 + n10
Find the sum of FITs for the BOPs.
Deadline: 3 days from today
Submission criteria: github, clean and clear code
есть кто понял задачу?

судя по всему просят предугадать формулу по введённому ряду и вернуть генератор. если ввели всего одно число, то очевидно что генератор будет выводить только это число если ввели 1, 2 - генератор должен предугадать, что следующие числа 3,4 если ввели 1, 2, 4 - генератор должен уже придумать что нибудь поинтереснее, по типу 7, 11 в качестве следующих элементов. n2, n3 - это номера генерируемых значений. Просят посчитать un = 1 - n + n2 - n3 + n4 - n5 + n6 - n7 + n8 - n9 + n10