In a study of the progeny of rabbits, fibonacci (ca. 1170-ca. 1240) encountered the sequence now bearing his name. the sequence is defined recursively as follows.

an + 2 = an + an + 1, where a1 = 1 and a2 = 1.
(a) write the first 12 terms of the sequence.

(b) write the first 10 terms of the sequence defined below. (round your answers to four decimal places.)

bn =
an + 1/
an, n ? 1.
(c) the golden ratio ? can be defined by
limn ? in a study of the progeny of rabbits, fibonacci (cbn = ?
, where
? = 1 + 1/? . solve this equation for ? . (round your answer to four decimal places.)