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Math Help - Sequences and Series, I am struggling and could use some guidance.

  1. #1
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    Question Sequences and Series, I am struggling and could use some guidance.

    I could really use some help with sequences and series. I don't understand how the equations are suppose to work. I seem to be struggling with the problems.

    State the first five terms of the sequence if a1=4 and an+1=-3an

    Find the 65th term of the sequence 9, 15, 21, 27,.....

    Find the sum of each infinate geometric series.
    -15+5+5/3+... _________
    E-4(3/4)n-1 ___________

    Find the Recursive and explicit (nth term) formulas for the sequence.
    -3, 4, 11, 18 Recursive: ____________Explicit: ____________

    Find 2 geometric means between 6 and 60.25.
    ________,__________
    Find 3 arithmetic means between -25 and 5
    ________,__________,_________

    Thanks in advance for the help.
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    is up to his old tricks again! Jhevon's Avatar
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    Please do not post the same question twice.

    Quote Originally Posted by power2600 View Post
    I could really use some help with sequences and series. I don't understand how the equations are suppose to work. I seem to be struggling with the problems.

    State the first five terms of the sequence if a1=4 and an+1=-3an


    We have a_1 = 4 and a_(n+1) = -3a_n
    Note that a_n is the term before a_(n+1)

    So the first five terms are:
    a_1 = 4
    a_2 = a_(1 + 1) = -3a_1 = -3(4) = -12
    a_3 = a_(2 + 1) = -3a_2 = -3(-12) = 36
    a_4 = a_(3 + 1) = -3a_3 = -3(36) = -108
    a_5 = a_(4 + 1) = -3a_4 = -3(-108) = 324

    Find the 65th term of the sequence 9, 15, 21, 27,.....
    Note that 15 – 9 = 21 – 15 = 27 – 21 = 6. so we have a common difference between the terms. Thus we have an arithmetic sequence. The terms of an arithmetic sequence is given by:
    a_n = a_1 + (n – 1)d, where a_n is the nth term, a_1 is the first term, n is the current number of the term, and d is the common difference. So for this sequence, we have:

    a_n = 9 + (n – 1)6 = 9 – 6 + 6n = 3 + 6n

    So the 65th term is a_65 = 3 + 6(65) = 393


    Find the sum of each infinate geometric series.
    -15+5+5/3+... _________
    For 15 + 5 + 5/3 + … I don’t think it should be a -15
    Note that these terms come from a geometric sequence with common ratio r = 1/3 and the first term a = 15. since |r|<1, the infinite sum is given by:

    S = a/(1 – r) = 15/(1 – 1/3) = 15/(2/3) = 45/2

    E-4(3/4)n-1 ___________


    For -4(3/4)^(n – 1), we have a geometric series with a = -4, r = , since |r|<1, again the infinite sum is given by:

    S = a/(1 – r) = -4/(1 – ) = -4/(1/4) = -16
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by power2600 View Post


    Find the Recursive and explicit (nth term) formulas for the sequence.
    -3, 4, 11, 18 Recursive: ____________Explicit: ____________

    Recursive: a_1 = -3, a_(n+1) = a_n + 7

    Explicit: a_n = -3 + 7(n - 1) for n = 1,2,3,4 ... or a_n = -10 + 7n for n = 1,2,3,4 ...
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