What is the recurrence relation for 1, 7, 31, 127, 499?
A. bn+1=5bn-1+3
B. bn=4bn+7!
C. bn=4bn-1+3
D. bn=bn-1+1
Answer:C
What is the recurrence relation for 1, 7, 31, 127, 499?
A. bn+1=5bn-1+3
 B. bn=4bn+7!
 C. bn=4bn-1+3
 D. bn=bn-1+1

Explanation: Look at the differences between terms: 1, 7, 31, 124,…. and these are growing by a factor of 4. So, 1⋅4=4, 7⋅4=28, 31⋅4=124, and so on. Note that we always end up with 3 less than the next term. So, bn=4bn-1+3 is the recurrence relation and the initial condition is b0=1.
