Math 242 Group Problems Section 9.1
1. The sequence {dn} gives the number of different ways to seat n guests at a round dining table.
(a) What does the seventh term of this sequence tell us about seating guests?
(b) Interpret d4 = 6.
(c) Use sequence notation to express the fact that there are 40,320 different ways to seat 9 people
at a round dinner table.
2. The terms of the sequence {cn} give the number of wine casks that can be stacked in a pyramid
structure using n casks on the bottom row.
(a) What does the fifth term of this sequence tell us about wine casks?
(b) If 1
2(1)
n
cnn=+, find c8 and explain its meaning in practical terms.
(c) Can you have a pyramidal stack of 100 wine casks? Explain why or why not.
(d) Write the first four terms of the sequence {cn}. These numbers are called triangular numbers.
(e) Find a recursive definition for this sequence.
Determine if the description of the relationship defines a sequence explicitly or recursively.
3. Each term is four more than the previous term.
4. Each term is one less than the square of its term number.
5. To find the nth term, add one to n, and then divide by n.
6. To find the nth term, subtract the two previous terms.