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​−a1​a3​−a2​⋯a100​−a99​​=2⋅1,=2⋅2,=2⋅99.​
Adding, one obtains
a100​−a1​a100​​=2(1+2+⋯+99)=99⋅100=9900,=9902.​