Problem:
If the sequence {an} is defined by
a1=2an+1=an+2n(n≥1)
then a100 equals
Answer Choices:
A. 9900
B. 9902
C. 9904
D. 10100
E. 10102
Solution:
From the definition of the sequence,
a2−a1a3−a2⋯a100−a99=2⋅1,=2⋅2,=2⋅99.
Adding, one obtains
a100−a1a100=2(1+2+⋯+99)=99⋅100=9900,=9902.