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  1. #1
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    Advanced Math

    Need help with these questions for a test review.



    7. Write the first five terms of the sequence defined by the recursive formula:

    t1 = 2 , tn = 1 / tn-1

    8. For the geometric series 6 + 3 + 3/2 + 3/4 + .... find: (leave you answer as a fraction in lowest terms)
    a) the tenth term
    b) the sum of the first ten terms



    9. In a geometric sequence t5 = 48 and t8 = 384. Find tn.

    10. Evaluate: 20 + 14 + 8 + ..... + (-70)

    11. In an arithmetic series t1 = 6 and S9 = 108. Find the common difference and sum of the first 20 terms.

    12. In an arithmetic series, S11 = 297 and S24 =1428, find tn.

    13. A doctor prescribes 200 mg of medication on the first day of treatment. The dosage is halved each day for one week. To the nearest milligram what is the total amount of medication taken by the patient after 1 week?
    Last edited by azeee100; April 8th 2009 at 04:56 PM. Reason: mistake
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  2. #2
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    Quote Originally Posted by azeee100 View Post
    Need help with these questions for a test review.



    7. Write the first five terms of the sequence defined by the recursive formula:

    t1 = 2 , tn = 1 / tn-1

    8. For the geometric series 6 + 3 + 3/2 + 3/4 + .... find: (leave you answer as a fraction in lowest terms)
    a) the tenth term
    b) the sum of the first ten terms



    9. In a geometric sequence t5 = 48 and t8 = 384. Find tn.

    10. Evaluate: 20 + 14 + 8 + ..... + (-70)

    11. In an arithmetic series t1 = 6 and S9 = 108. Find the common difference and sum of the first 20 terms.

    12. In an arithmetic series, S11 = 297 and S24 =1428, find tn.

    13. A doctor prescribes 200 mg of medication on the first day of treatment. The dosage is halved each day for one week. To the nearest milligram what is the total amount of medication taken by the patient after 1 week?
    These look pretty basic... have you tried any at all?
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    First see: Arithmetic progression - Wikipedia, the free encyclopedia

    and

    Geometric progression - Wikipedia, the free encyclopedia

    Quote Originally Posted by azeee100 View Post
    7. Write the first five terms of the sequence defined by the recursive formula:

    t1 = 2 , tn = 1 / tn-1
    please use parentheses!

    i am sure you meant t_n = \frac 1{t_{n - 1}}. in that case, type: t_n = 1/t_(n - 1) or better yet, use {} brackets. even better, use {} brackets and put LaTeX tags around everything. see the last link in my signature.

    anyway, if you're about to do a test, surely you can at least do this type of problem by now.

    you want the list t_1,~t_2,~t_3,~t_4,~t_5

    for t_2, plug in n = 2 in the formula for t_n. here you get t_{\color{red}2} = \frac 1{t_{{\color{red}2} - 1}} = \frac 1{t_1} = \frac 12

    now do the same for the others.

    8. For the geometric series 6 + 3 + 3/2 + 3/4 + .... find: (leave you answer as a fraction in lowest terms)
    a) the tenth term
    b) the sum of the first ten terms
    see the second link i gave you at the start of this thread. here, your a = 6 and your r = 1/2

    9. In a geometric sequence t5 = 48 and t8 = 384. Find tn.
    again, see the second link for the general form. and apply a similar method to the one used here to find t_n

    10. Evaluate: 20 + 14 + 8 + ..... + (-70)
    see the first link i gave you at the beginning of this thread. here a_1 = 20 and d = -6

    11. In an arithmetic series t1 = 6 and S9 = 108. Find the common difference and sum of the first 20 terms.
    again, see the first link i gave

    12. In an arithmetic series, S11 = 297 and S24 =1428, find tn.
    ditto

    13. A doctor prescribes 200 mg of medication on the first day of treatment. The dosage is halved each day for one week. To the nearest milligram what is the total amount of medication taken by the patient after 1 week?
    note that the dosage follows a geometric sequence, with a = 200 and r = \frac 12. you want the sum of the first 7 terms of this sequence
    Last edited by Jhevon; April 8th 2009 at 05:47 PM.
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    Quote Originally Posted by Jhevon View Post

    you want the list t_1,~t_2,~t_3,~t_4,~t_5

    for t_2, plug in n = 2 in the formula for t_n. here you get t_{\color{red}2} = \frac 1{t_{{\color{red}2} - 1}} = \frac 1{t_1} = 1

    now do the same for the others.
    Actually it's...

    t_2 = \frac{1}{t_1} = \frac{1}{\color{red}2}.
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Prove It View Post
    Actually it's...

    t_2 = \frac{1}{t_1} = \frac{1}{\color{red}2}.
    yes, fixed it
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