4 + 12/a + 36/a^2 + 108/a^3 + 324/a^4.................If a=4, then by convergence test we get:
[4+∑(4*3^n)/4^n)), n=1 to ∞] =16, so a=4 is correct. The infinite series: 4/(1 - r)=16, r=3/4.
Source: http://www.wolframalpha.com/input/?i=%5B4%2B%E2%88%91(4*3%5En)%2F4%5En)),+n%3D1+to+%E2%88%9E%5D