  In this paper we provided a formula for the $n$th term of the $k$-generalized
Fibonacci-like sequence, a generalization of the well-known Fibonacci sequence,
having $k$ arbitrary initial terms, where the succeeding terms are obtained by
adding its previous $k$ terms. The formula for the $n$th term of the
$k$-generalized Fibonacci-like sequence was obtained by observing patterns in
the derived formula for the nth term of the Fibonacci-like, Tribonacci-like,
and Tetrabonacci-like sequence. The formula for the $k$-generalized Fibonacci
sequence was also derived and was used in the process of proving the main
result of this paper.
