An Algebra II Turvy to Review Sequences and Series

 

 

A Turvy is a Drawing which has a caption right side up

and has another caption if you turn it topsy-turvy.

 

 

 

Caption for the picture:

 

      "__ __ __ __ __ __ __    __ __ __ __    __ __ __ __ __ __ __    __ __ __ __ __."

       14   8  17  7  14 17  3    12   1 16   2      8  1810 10  14  3   4     11 14 15 15 17

 

 

 

Caption for the picture turned upside down:

 

 

             "__ __ __ __ __  -  __ __    __ __    __    __ __ __ __ __ __ __ 

              12   7  18 10 16      5  11    18  2     17    12 17 13 13 17  4  16

 

                                          __ __ __ __ __    __ __ __."

                                          11 17  8  12  1      9  14  6

 

 

 

 

To determine the titles to this turvy, solve the 18 problems about sequences and series. 

Then find the answers to each problem from the choices below.

Then replace each numbered blank with the letter corresponding to the answer for that problem.

 

 

___  1. Determine the sum of the infinite series     

 

___  2. If the 6^th term of an arithmetic sequence is 8 and the 11^th term is 2,

             what is the first term?

 

___  3. Find   in the sequence  1, 4, 7, 10, …

 

___  4. Determine the sum of the first 8 terms of the geometric sequence

 

                         

 

___  5. Insert 4 geometric means between 160 and 5.  What is the first of these geometric

             means?

 

___  6. Determine the 5^th term of the geometric sequence

 

                         

 

___  7. The 4^th term of a geometric sequence is  and the 6^th  term is .  Find the

              common ratio.

 

___  8.  Determine the sum of the infinite series        

 

___  9. A person has 2 parents, 4 grandparents, 8 great-grandparents, and so on.

            Determine the number of his ancestors during the 8 generations preceding

             his own (provided that there are no duplications).

 

___ 10. Determine the sum of the first 25 positive even integers.

 

___ 11. Determine the sum of the arithmetic series   5 + 9 + 13 + .. + 401.

 

___ 12. Insert 4 arithmetic means between 1 and 36.Determine the first of these

              arithmetic means.

 

___ 13. If the 7^th term of a geometric sequence is 192 and r = 2, determine the first term.

 

___ 14. Determine the sum of the first ten terms of the geometric sequence

                  15,  30,  60,  120,  …

 

___ 15. Determine the value of   for the sequence    6,  1,  -4,  …

 

___ 16. Evaluate    

 

___ 17. If the 6^th term of an arithmetic sequence is 9 and the 11^th term is  -1, what is the

             first term?

 

___ 18. If the 1^st term of an arithmetic sequence is 4 and the 12^th term is 32, find the

              common difference.

 

 

 

 

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ANSWERS:

 

a. 19                                        h.                                        o.  

 

 

b. 3                                          i. 15,345                                  p. 20,300

 

 

c. 8                                          j.  17                                        s. 650

 

           

d.                                       k. 510                                      t. 15

 

 

e. 27                                        l.                               u. 80

 

 

f. 18                                         m. 0                                         w. 81

 

 

g.                                     n. 28                                        z. -74