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 a_n+2 = a_n + a_n+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 by

(c) Using the definition in part (b), show that

(d) The golden ratio ρ can be defined by

Show that ρ = 1 + (1/ρ) and solve this equation for ρ.

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b₁ an+1 an n ≥ 1.