Example: {1,2,4,8,...} The sequence starts at 1 and doubles each time, so. a=1 (the first term); r=2 (the "common ratio" between terms is a doubling). And we get: {a, ar, ar2, ar3, ... } = {1, 1×2, 1×22, 1×23, ... } = {1, 2, 4, 8, ... } But be careful, r should not be 0: When r=0, we get the sequence {a,0,0,...} which is not geometric ...
