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Math Help - Sequences.. ?

  1. #1
    Junior Member
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    Question Sequences.. ?

    Dear All,

    I need help to solve these questions on sequences..

    Q1. Write the first rour terms of the following sequences
    If
    i) a_n = (-1)^n (2n-3)

    ii) a_n - a_{n-1} = n + 2, a_1 = 2


    Q2. Which term of the arithmetic sequence -2, 4, 10, .... is 148?

    Q3. Find the 11th term of the sequence 1+i, 2, 4/1+i, .... where i^2 = -1


    Answers with some description will help me to understand the methodology.

    Thanks in Advance
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by cu4mail View Post
    Dear All,

    I need help to solve these questions on sequences..

    Q1. Write the first rour terms of the following sequences
    If
    i) a_n = (-1)^n (2n-3)

    ii) a_n - a_{n-1} = n + 2, a_1 = 2
    all you have to do is to replace n by 1, 2, 3, and 4..

    Quote Originally Posted by cu4mail View Post
    Q2. Which term of the arithmetic sequence -2, 4, 10, .... is 148?
    note that a_n = a_1 + (n-1)d, where d is the common difference.. you see in the sequence that a_1 = -2 and d=6. so,
    a_n = 146 = -2 + (n-1)6. solve for n.


    Quote Originally Posted by cu4mail View Post
    Q3. Find the 11th term of the sequence 1+i, 2, 4/1+i, .... where i^2 = -1


    Answers with some description will help me to understand the methodology.

    Thanks in Advance
    note that \frac{2}{1+i} = \frac{\frac{4}{1+1}}{2} so that the sequence is Geometric..
    so use the formula a_n = a_1 r^{n-1}, where r is the common ratio..
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  3. #3
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    Quote Originally Posted by kalagota View Post
    note that \frac{2}{1+i} = \frac{\frac{4}{1+1}}{2} so that the sequence is Geometric..
    so use the formula a_n = a_1 r^{n-1}, where r is the common ratio..
    Actually \frac{2}{1+i} = { 1-i }
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