What type of sequence is the sequence represented by the sum of the terms that has the resul 2^n - 1 ?

First, we need to determine the general term of the
sequence, bn, and then, we'll utter any other term of the
progression.

From
enunciation:

Sn=b1+b2+b3+...+bn

(2^n)-1=b1+b2+b3+...+bn

bn=(2^n)-1-[b1+b2+b3+...+b(n-1)]

But
[b1+b2+b3+...+b(n-1)]=S(n-1)=[2^(n-1)]-1

bn = Sn -
S(n-1)

bn = (2^n) - 1 - 2^(n-1) +
1

We'll eliminate like terms and we'll factorize by
2^n:

bn=2^n(1-1/2)=2^n*1/2=2^(n-1)

Since
we know the general term bn, we'll compute the first 3 consecutive terms,
b1,b2,b3.

b1=2^(1-1) = 2^0 =
1

b2=2^(2-1) = 2 =
2*b1

b3=2^(3-1) =
2^2=2*b2

Sn = 2^n - 1 is the sum of the terms
of a geometric sequence, whose common ratio is q =
2.