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  1. #1
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    Advanced functions question help

    I need help with these advanced functions problems

    State the Common Ratio of the following Geometric sequence
    3/4 , 3/10 , 3/25 , 6/125

    2. In the Arithmetic Sequence below, X = ___
    100 , ___ , _X_ , 64

    3. For the Geometric Sequence below, X = ___
    _X_ , 48 , ___ , ___ , 6

    4. Given the sequence 15 , 9 , 3 , -3 ... t 20 = ___

    5. Given the sequence 27/8 , 9/4 , 3/2 , 1 ... t 14 = ___ (write as a fraction)

    6. State the next 3 terms and state the pattern in WORDS:
    a) 4, 9, 15, 22, ....
    b) 1, -3, 9, -27, ....

    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 temour123; March 23rd 2009 at 06:38 PM. Reason: f
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  2. #2
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    Quote Originally Posted by temour123 View Post
    I need help with this advanced functions problem

    The first term in a sequence of number is t1 = 5. The terms that follow are defined by the formula: tn - tn-1 = 2n +3. Determine the value of t50.
    Hi temour123,

    I'm having a little difficulty deciphering your notation. Is this what you have?

    t_1=5 (First Term)

    t_n-t_{n-1}=2n+3 (Common Difference)

    If the 1st term is 5, then the 2nd term will be 2(2)+3=7, etc. So, the common difference (d) is 2.

    Use this formula to calculate the nth term (50th) term:

    t_n=t_1+(n-1)d

    t_{50}=5+(50-1)2
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  3. #3
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    Hello,
    Quote Originally Posted by masters View Post
    Hi temour123,

    I'm having a little difficulty deciphering your notation. Is this what you have?

    t_1=5 (First Term)

    t_n-t_{n-1}=2n+3 (Common Difference)

    If the 1st term is 5, then the 2nd term will be 2(2)+3=7, etc. So, the common difference (d) is 2.

    Use this formula to calculate the nth term (50th) term:

    t_n=t_1+(n-1)d

    t_{50}=5+(50-1)2
    No !

    t_2-t_1=2(2)+3=7 \Rightarrow t_2=5+7=12

    This is not a simple arithmetic progression !




    You can see that t_n-t_1=t_n-t_{n-1}+t_{n-1}-t_{n-2}+t_{n-2}-\dots+t_2-t_1=\sum_{k=2}^{n} [t_k-t_{k-1}]=\sum_{k=2}^n [2k+3]

    t_n-t_1=2 \sum_{k=2}^n k+3 \sum_{k=2}^n 1=2 \left(\sum_{k=1}^n k-1\right)+3 (n-1)=2 \left(\frac{n(n+1)}{2}-1\right)+3(n-1)

    t_n-5=2 \left(\frac{n^2+n-2}{2}\right)+3n-3

    Thus t_n=n^2+n-2+3n-3+5=n^2+4n=n(n+4)

    then just let n=50
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    reply

    yea your write whatever your doing
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  5. #5
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    Quote Originally Posted by temour123 View Post
    1. Halley's comet appears in the sky approximately once every 77 years. If the comet was seen in by Astronomer Edmund Halley in 1531. How many times has the comet been spotted since?
    What is the number of years between 2009 and 1531? (Hint: Subtract.)

    How many periods of 77 fit within this period? (Hint: Divide, and ignore the remainder.)

    Quote Originally Posted by temour123 View Post
    2. The disappearance of dinosaurs occurred about 65 million years ago. Scientists have found that mass extinction's occur roughly every 26 million years apart. If this theory is correct, estimate when the next mass extinction should occur.
    What is 65 - 26? What do you get if you subtract 26 from that result?

    Quote Originally Posted by temour123 View Post
    3. Canada's population 32.8 million and is growing by approximately 1% per year. Predict the population of Canada in 10 years.
    If you are familiar with the compounded-growth formula, A = P(1 + r/n)^(nt), use that, with P = 32.8, r = 0.01, n = 1, and t = 10. Otherwise, find one percent of 32.8, and add this to 32.8. Then find one percent of that, and add it to your previous total. Keep going until you've done ten years' worth.

    Quote Originally Posted by temour123 View Post
    4. Ice Dreams finds its profit from the sale of ice cream increases by $30 per week during the 9 weeks of student summer holidays. Find the profit for the summer season if the profit for the first week of the summer is $100.
    If the first week was $100 and the next week was $30 more, then what what the second week?

    If the next week was $30 more, then what was the third week?

    Keep going, until you have the values for each of the nine weeks.

    Then add the nine values to get the total for the summer.

    Quote Originally Posted by temour123 View Post
    5. During the two months of the summer holiday, you find a summer job that pays $160 per week with a $10 a week raise. How much money will be made by the end of the summer?
    This one work very much like exercise (4) above.

    Quote Originally Posted by temour123 View Post
    6. Your grandmother offers you $1 on the first day of March break and offers to double it each day of the break to help her with chores in her house. If you were to help her for 7 days over the break, how much money would you get at the end of day 7?
    This one works similarly to exercises (4) and (5), except that you're multiplying each time, instead of adding.

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