Exercises


  1. Jolie says, "The general term of a sequence is term number \(+~20\)." Does Jolie's statement contain enough information to describe the sequence?  If so, what is the \(8^{th}\) term in the sequence?
  2. Find the general term for each of the following sequences:
    1. \(31,~32,~33,~34, \ldots\)
    2. Term 1 has 3 hearts, term 2 has 4 hearts, term 3 has 5 hearts, and term 4 has 6 hearts.
  3. Consider the following sequences:
    Sequence 1
    \(2,~3,~4,~5,~6,\ldots\)
    Sequence 2
    \(10,~11,~12,~13,~14,\ldots\)
    Sequence 3
    \(13,~14,~15,~16,~17,\ldots \)
    1. State the pattern rule and general term for each of the above sequences.  
    2. What do the three general terms have in common, and how do they differ?
    3. Describe a procedure that will allow you to find the general term of any sequence that is similar to the three sequences given.
  4. A grandfather clock in Jodie's home chimes once at one o'clock, twice at two o'clock, and so on.  If there are no chimes except for at the beginning of each hour, how many times does the clock chime during the \(12\)-hour period between 12:30 pm and 12:30 am?
  5. Alex is trying to fill his gold fish tank. After filling his tank for one hour it contained \(5\) litres of water.  The tank will gain \(1\) litre of water each hour after that. That is, the tank will contain \(6\) litres of water after two hours, \(7\) litres of water after three hours, and so on.
    1. Find the general term to describe how much water is in the tank after a certain "number of hours."
    2. If the tank has a capacity of \(20\) litres, how many hours will it take to fill the tank?
  6. A patient who is recovering from a heart attack is about to start a regular walking program.  The patient is told to walk a distance of \(3\) km in the first week, \(4\) km in the second week, \(5\) km in the third week, and so on, adding \(1\) km every week.
    1. Find the general term of the sequence representing the distance walked each week.
    2. After the \(10^{th}\) week, the patient is asked to maintain this distance for the remainder of the recovery.  How far will the patient walk during the \(10^{th}\) week, and every week thereafter?
    3. What is the total distance that the patient will walk over the first \(24\) weeks of the walking program?
  7. Consider the sequence that begins with the terms \(-6,-5,-4,-3,\ldots\)
    1. What is a pattern rule for this sequence? Using this pattern rule, write the next four terms in the sequence.
    2. Write the general term for this sequence. What is the \(20^{th}\)  term in this sequence?
    3. What is the sum of the first \(16\) terms in this sequence?