Problem:
The sequence S1​,S2​,S3​,…,S10​ has the property that every term beginning with the third is the sum of the previous two. That is,
Sn​=Sn−2​+Sn−1​ for n≥3
Suppose that S9​=110 and S7​=42. What is S4​ ?
Answer Choices:
A. 4
B. 6
C. 10
D. 12
E. 16
Solution:
Note that 110=S9​=S7​+S8​=42+S8​, so S8​=110−42=68. Thus 68=S8​=S6​+S7​=S6​+42, so S6​=68−42=26. Similarly, S5​=42−26=16, and S4​=26−16=10​.
The problems on this page are the property of the MAA's American Mathematics Competitions