Question

Consecutive pairs of numbers in the Fibonacci sequence have approximately the same ratio to one another.Using this approximation, if 1597 follows 987 in the Fibonacci sequence, what follows 4181? Round to thenearest whole number.

Answer 1

The first step is to find the common ratio of connsecutive terms in the Fibonacci sequence. From the given sequence, the consecutive terms are 1597 and 987

Common ratio, r = 1597/987 = 1.6180344478

Let x be the number that follows 4181. The common ratio is the same. Thus,

x/4181 = r = 1.6180344478

By crossmultiplying,

x = 4181 x 1.6180344478

x = 6765

The number that follows 4181 is 6765