Given the sequence: {2, 8, 32, 128, 512…}, s12 =

In mathematics, the arrangement of numbers that have a definite pattern is a progression. There are three types of progression: arithmetic, harmonic and geometric. Arithmetic sequence have a common difference, harmonic sequence is the reciprocal of arithmetic sequence, and geometric sequence have a common ratio. For this problem, it is a geometric sequence. 

8/2 = 4
32/8 = 4
128/32 = 4
512/128 = 4

The common ratio is 4. The equation for geometric sequence for the sum of terms is:



where n is the last term of the progression
A1 is the first term of the progression
r is the common ratio 

Substituting the values,


S12 = 11,184,810

11/36 is .305 repeating

The total would be 40.53