**Solution:**

Let the G.P. be *a*, *ar*, *ar*^{2}, *ar*^{3}, …

According to the given condition,

*a *+ *ar* + *ar*^{2} = 16 and *ar*^{3} + *ar*^{4} + *ar*^{5} = 128

⇒ *a* (1 + *r* + *r*2) = 16 … (1)

*ar*^{3}(1 + *r* + *r*2) = 128 … (2)

Dividing equation (2) by (1), we obtain

Substituting *r* = 2 in (1), we obtain

*a* (1 + 2 + 4) = 16

⇒ *a* (7) = 16