Assignment:
Q1) Find and solve a recurrence relation for the number of n-digit ternary sequences with no consecutive digits being equal.
Q2) 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.
Q3) 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.)
Q4) 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 Initially there is $1000 in the account, and in year k, $10k are withdrawn.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?
Q5) 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.
Provide complete and step by step solution for the question and show calculations and use formulas.