Question

Find S11 for 1 + 2 + 4 + 8 +

Answer 1

Evaluating the given sequence, it is evident that the next number is twice the number prior to it. Thus, the given is a geometric sequence with first term (a1) equal to 1 and common ratio of 2. The geometric series may be calculated by the equation,
 
                                            Sn = a1 x (1 - r^n) / (1 - r)

where Sn is the sum of n terms in this case, n = 11. 
Substituting the known values, 
 
                                      Sn = 1 x (1 - 2^11) / (1 - 2) = 2047

Thus, S11 is 2047.