2) Find and solve a recurrence relation for the number of infinite regions formed by n infinite lines drawn in the plane so that each pair of lines intersects at a different point.
3) Find and solve a recurrence relation for the number of different regions formed when n mutually intersecting planes are drawn in three-dimensional space such that no four planes intersect at a common point and no two planes have parallel intersection lines in a third plane. (Hint: reduce to a two-dimensional problem.)
4) Suppose a savings account earns 5 percent a year. Initially there is $1000 in the account, and in year k, $10k are withdrawn. How much money is in the account at the end of n years if:
A) Annual withdrawal is at year's end?
B) Withdrawal is at start of year?
5) Find and solve a recurrence relation for the number of n-digit ternary sequences in which no 1 appears to the right of any 2.
Recurrence Relations and Lines and Planes; Savings and Interest; n-Digit Ternary Sequences are investigated. The solution is detailed and well presented.