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# Recurrence Relations : Lines and Planes; Savings and Interest; n-Digit Ternary Sequences

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1) Find and solve a recurrence relation for the number of n-digit ternary sequences with no consecutive digits being equal.

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 Initially there is \$1000 in the account, and in year k, \$10k are withdrawn.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.