148k views
0 votes
The Fibonacci sequence given in (7) is defined recursively using addition. Is it an arithmetic sequence? Explain.

1 Answer

1 vote

Final answer:

The Fibonacci sequence is not an arithmetic sequence because the difference between consecutive terms is not constant, despite the fact that addition is commutative.

Step-by-step explanation:

The Fibonacci sequence is defined by the relation F(n) = F(n-1) + F(n-2), with seed values F(0)=0 and F(1)=1. This sequence is not an arithmetic sequence because the difference between consecutive terms is not constant. For example, the first few terms of the Fibonacci sequence are 0, 1, 1, 2, 3, 5, 8, 13, and so on. The differences between consecutive terms are 1, 0, 1, 1, 2, 3, 5, which are not constant. Additionally, while addition is commutative (meaning A + B = B + A), which holds true for regular numbers as well as in the context of vector addition, this property alone does not make a sequence arithmetic.

User Katmanco
by
6.8k points