Let \(\{w_n(a,b;p,q)\}\) be the generalized Fibonacci sequence \[ w_0 = a, w_1 = b, w_n = pw_{n-1} + qw_{n-2} \text{ for } n \geq 2, \] where \(q, b, p, q\) are arbitrary complex numbers and \(q \geq 0\). Explicit formulae of sums \[ \sum_{i=0}^n w_{r+ti}(a,b;p,q),\quad\sum_{i=0}^n (-1)^i w_{r+ti}(a,b;p,q),\quad \sum_{i=0}^n k^i w_{r+ti}(a,b;p,q), \] \[ \sum_{i=0}^n {n\choose i} w_{r+ti}(a,b;p,q),\quad \sum_{i=0}^n (-1)^i {n\choose i} w_{r+ti}(a,b;p,q),\quad \sum_{i=0}^n (i+1) w_{r+ti}(a,b;p,q), \] \[ \sum_{i=0}^n (-1)^i (i+1) w_{r+ti}(a,b;p,q),\quad \sum_{i=0}^n k^i (i+1) w_{r+ti}(a,b;p,q) \] are given, where \(k\) is an arbitrary complex number, \(n, r \geq 0\) and \(t > 0\) are arbitrary natural numbers.