$S_1$=a, $S_2$=b, $S_n$=|$S_{n-1}$-$S_{n-2}$|(n $\ge$3). Can I compute the formula of $S_n$? Thanks in advance.
2026-05-15 13:29:49.1778851789
How to compute the formula of $S_n$
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If $b=qa+r$, then the sequence is
$a,b, (q-1)a+r, a, (q-2)a+r, (q-3)a+r, a, (q-4)a+r, (q-5)a+r, a, \dots$
eventually you get to two consecutive terms that are $a, r$ or $r,a$, and you repeat. Thus you basically get the sequence from Euclid's Algorithm. That is, the sequence eventually ends with
$gcd(a,b), gcd(a,b), 0,gcd(a,b), gcd(a,b), 0, \dots$