Can you adapt this
n=3;
rx=Table[Sum[If[j<i,1,1/2]*I*Sin[Subscript[\[Phi],j]],{j,1,i}],{i,1,n}];
ry=Table[Sum[If[j<i,1,1/2]*I*Cos[Subscript[\[Phi],j]],{j,1,i}],{i,1,n}];
and then rx has the value
{(I/2)*Sin[Subscript[\[Phi], 1]],
I*Sin[Subscript[\[Phi], 1]] + (I/2)*Sin[Subscript[\[Phi], 2]],
I*Sin[Subscript[\[Phi], 1]] + I*Sin[Subscript[\[Phi], 2]] + (I/2)*Sin[Subscript[\[Phi], 3]]}
and ry is similar with Cos
If you only wish to use For then
n=3;
rx=Table[0,{n}];
For[i=1,i<=n,i++,
For[j=1,j<=i,j++,
rx[[i]]=rx[[i]]+If[j<i,1,1/2]*I*Sin[Subscript[\[Phi],j]]
]
];
will give you the same values for rx and similar code with Cos will give you the same values for ry