FoldPairList

FoldPairList[f, y0, {a1, a2, ...}] gives the list of successive xi obtained by applying f to pairs, where f returns {xi, yi} at each step.

Examples

Running total with outputs:

FoldPairList[{#1 + #2, #1 + #2} &, 0, {1, 2, 3, 4}]
(* {1, 3, 6, 10} *)

Generate Fibonacci-like sequence:

FoldPairList[{#1, #1 + #2} &, 1, Range[6]]

Please visit the official Wolfram Language Reference for more details.