(a_3=16=ar^2), (a_6=-128=ar^5)

[ \dfrac{ar^5}{ar^2}=r^3=\dfrac{-128}{16}=-8\implies r=-2 ] [ a(-2)^2=16\implies 4a=16\implies a=4 ]

[ S_7 = a\dfrac{1-r^7}{1-r}=4\dfrac{1-(-2)^7}{1-(-2)}=4\dfrac{1-(-128)}{3}=4\cdot\dfrac{129}{3}=172 ]

Answer: First term (=4); (S_7=172)