{1, -2, 3, -4, 5, -6, 7, -8, 9, -10}
{1, -1, 1, -1, 1, -1, 1}
Another try
In[47]:= o = 0; Range[10] /. x_Integer :> (-1)^Mod[o++, 2] x Out[47]= {1, -2, 3, -4, 5, -6, 7, -8, 9, -10} In[46]:= o = 0; ConstantArray[1, 7] /. x_Integer :> (-1)^Mod[o++, 2] x Out[46]= {1, -1, 1, -1, 1, -1, 1}
Try:
-(-1)^Range[10]Range[10] -(-1)^Range[10]