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Math Help - [SOLVED] Arithmetic and Geometric progressions

  1. #1
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    [SOLVED] Arithmetic and Geometric progressions

    Having a bit of trouble when it comes to these questions, any help is very much appreciated

    Q1. Programming languages such as miranda and Q use the notations [a..b] and [a,b..c] to represent finite sequences. For example, [1..5] is the sequence{1,2,3,4,5} and [1,3..11] is the sequence {1,3,5,7,9,11} (ie the 3 is the second term) For each of the notations [a..b] and [a,b..c], give a formula for the number of terms n of the sequence in terms of a,b and c.

    Q2. (a) Are the terms of the sequence Un = {log2,log2^2,log2^3} in arithmetic or geometric progression? What about Vn={(log2),(log2)^2,(log2)^3}?
    (b) Find the sum of the first 10 terms of both Un and Vn.
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  2. #2
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    Quote Originally Posted by Webby View Post

    Q2. (a) Are the terms of the sequence Un = {log2,log2^2,log2^3} in arithmetic or geometric progression? What about Vn={(log2),(log2)^2,(log2)^3}?
    (b) Find the sum of the first 10 terms of both Un and Vn.

    (a) U_n= log2,2log2,3log2,... , d=log 2 , thus it is an AP .

    V_n=(log2),(log2)^2,(log2)^3,... , r=log2 , it is a GP .

    They are both different .

    (b) Use the formulas of sum of AP and GP respectively .
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  3. #3
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    Hello, Webby!

    Q2. (a) Are the terms of the sequence U_n \:=\:\log2,\;\log(2^2),\:\log(2^3),\:\hdots
    in arithmetic or geometric progression?

    We have: . \log 2,\:2\log2,\:3\log2,\:\hdots

    This is an arithmetic sequence with first term, a = \log 2,
    . . and common difference, d = \log 2




    (b) What about: V_n\:=\:(\log2),\:(\log2)^2,\:(\log2)^3,\:\hdots

    This is a geomtric sequence with first term, a = \log 2
    . . and common ratio, r = \log 2




    (c) Find the sum of the first 10 terms of both U_n and V_n.

    For U_n\!:\;\;S_{10} \:=\:\frac{10}{2}\bigg[2\log 2 + 9\log2\bigg] \:=\:55\log2

    For V_n\!:\;\;S_{10} \:=\:(\log2)\frac{1-(\log 2)^{10}}{1-\log2}

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