<prompt> Mfuatano a_n umefafanuliwa na a_0 2, a_1 1, naa_n a_n - 1 sqrt3 - a_n - 2kwa n zote ge 2. Pata a_100.  <response>: Tuna hiyoanzaaligna_2 sqrt3 - 2, a_3 sqrt3 - 2 sqrt3 - 1 2 - 2 sqrt3, a_4 2 - 2 sqrt3 sqrt3 - sqrt3 - 2 sqrt3 - 4, a_5 sqrt3 - 4 sqrt3 - 2 - 2 sqrt3 1 - 2 sqrt3, a_6 1 - 2 sqrt3 sqrt3 - sqrt3 - 4 -2, a_7 -2 sqrt3 - 1 - 2 sqrt3 -1, a_8 -1 sqrt3 - -2 2 - sqrt3, a_9 2 - sqrt3 sqrt3 - -1 2 sqrt3 - 2, a_10 2 sqrt3 - 2 sqrt3 - 2 - sqrt3 4 - sqrt3, a_11 4 - sqrt3 sqrt3 - 2 sqrt3 - 2 2 sqrt3 - 1, a_12 2 sqrt3 - 1 sqrt3 - 4 - sqrt3 2, a_13 2 sqrt3 - 2 sqrt3 - 1 1.endalignKwa vile a_12 a_0 2 na a_13 a_1 1, na kila neno linategemea tu masharti mawili ya awali, mfuatano ni wa mara kwa mara kuanzia hapa na kuendelea, na kipindi cha urefu 12. Kwa hivyo, a_100 a_4 sqrt3 - 4. 