Abstract
The initial conditions of the Fibonacci and Lucas sequences can be used to generate a new number sequence. The new number sequence has a similar form and pattern to the recursive formula of the Fibonacci sequence. It is shown from the recursive formula of the new number sequence which is similar to the recursive formula of the Fibonacci sequence. The new number sequence is called as the Fibonacci-like sequence. The variations of the Fibonacci-like sequence are, inter alia, the Fibonacci and Fibonacci-like sub-sequences. The existences of the properties of the Fibonacci-like sequence and both variations, such as the convergence to the golden ratio, the Binet formula form, and the relative prime property, will be investigated.