THE FIBONACCI SEQUENCE In the Liber Abaci, Fibonacci posed the following problem about the number of offspring produced by a pair of rabbits: "A man put one pair of rabbits in a certain place entirely surrounded by a wall. How many pairs of rabbits can be produced from that pair in a year, if the nature of these rabbits is such that every month each pair bears a new pair which, from the second month on, becomes productive?" Assuming that none of the rabbits dies, a pair is born during the first month, so there are two pairs present. During the second month, the original pair produces another pair. One month later, both the original pair and the firstborn pair produce new pairs, so that there are three adult pairs and two young pairs. This process continues in the same way. The important point is that each month the young pairs mature and become adult pairs. Therefore, the new number of adult pairs is equal to the previous number of adult pairs plus the previous number of young pairs. Also, each pair that was adult in the previous month produces one young pair, so the new number of young pairs equals the previous number of adult pairs. When continued indefinitely, the sequence that arises from the rabbit problem is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, … This is called the Fibonacci sequence, and its terms are called Fibonacci numbers. The position of each number in the sequence is traditionally indicated by a subscript. Thus, u₁ = 1, u₂ = 1, u₃ = 2, and so on, where uₙ denotes the nth Fibonacci number.