The GEB\:sequence\:1,3,7,12,\dots is defined by the following properties:\ \qquad (i) the GEB sequence is increasing (that is, each term is larger than the previous term),\ \qquad (ii) the sequence formed using the di erences between each pair of consecutive terms in the GEB sequence (namely, the sequence 2,4,5;\dots) is increasing, and\ \qquad (iii) each positive integer that does not occur in the GEB sequence occurs exactly once in the sequence of differences in (ii).\What is the 100th term of the GEB sequence?
Answer Choices
A. 5751
B. 5724
C. 5711
D. 5777
E. 5764