Math 3113, Section 4

Fall 1999

Review questions on Chapter 1

NOTE: It is also strongly recommended to review past homework problems and your notes from group work in class.
It is not claimed that the problems on this page represent every type of question that could occur on the test.
But also note that this review sheet is definitely longer than the test will be!

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  1. Determine whether each of the following sequences is arithmetic or geometric.

    2. Find the initial term, the recursion and the explicit formula.
    1. {an} = {2, 5, 8, 11, ... }
    2. {bn} = {2, 6, 18, 54, ... }
    3. {cn} = {3, -1, -5, -9, ... }
    4. {fn} = {a2, a5, a8, a11, ... }, where an is as given above.

      5.  
  2. In each case, use the recursion to calculate the first six terms of each sequence:
    1. a1 = -3, an = an-1 + 5 for n > 2.
    2. b1 = 6, bn = bn-1/ 2 for n > 2.
    3. p1 = 1, p2 = 2; pn = pn-1·pn-2 -1 for n > 3.

      4.  
  3. Given the recursion and initial term, find the explicit formula:
    1. a1 = 3; an = an-1 - 2
    2. g1 = 7; gn = 2·gn-1

      3.  
  4. Given the following arithmetic sequence, find the sum (i)by adding backward and forward,

    5. and (ii)by using the formula 1 + 2 + 3 + ... + (n-1) + n = n(n+ 1)/ 2:
    1. {2, 5, 8, ... , 92, 95, 98}
    2. {a1 , a2 , a3 ,... , an },  where  ak = a1 + (k-1)d for k = 1, 2, ..., n

      3.  
  5. Find the sum of the even integers starting with 500 and ending with 800.

    6.  
  6. Find the sum of the first 20 terms of each of the following sequences:
    1. {gn} = {3, 6, 12, ... }
    2. {hn} = {1, 5, 25, 125, ... }

      3.  
  7. Find the sum of the first nterms of each of the following sequences:
    1. {gn} = {1, 2/ 3, 4/ 9, 8/ 27, ... }
    2. {hn} = {1, 0.9, 0.81, 0.729, ... }

      3.  
  8. In each of the sequences of problem 7, determine what happens to the value of the sum as ntends to infinity.

    9.  

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