Please find the general term of the sequence: 11,20,42,101,245,570,.... Thank for your help.?

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  • 1 month ago

    The next term cannot be found.

    Explanation

    The sequence is neither arithmetic nor geometric.

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  • 1 month ago

    The following is my work:

    11,20,42,101,245,570,.....,T(n),...

     .9,..22,.59,144,.325,.... D1

    ....13,.37,.85,.181,.....D2

    ......24,.48,.96,......D3

    D3 can be rewritten as 24, 24*2,24*2^2,...

    This results suggest a pattern that

    T(n)=an^2+bn+c+d[2^(n-1)]

    =>

    a+b+c+d=11

    4a+2b+c+2d=20

    9a+3b+c+4d=42

    16a+4b+c+8d=101

    Solving the system, get

    a=-5.5

    b=1.5

    c=-9

    d=24

    Thus, T(n)=24[2^(n-1)]-5.5n^2+1.5n-9.

    Check: 

    11...20...42...101...245...570...1268...2723...5703...T(10),...

     .. 9...22....59....144....325...698....1455...2980...D1

    ......13...37....85.....181...373...757.....1525....D2

    ..........24...48....96.....192...384....768.....D3

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  • 1 month ago

    The nth term of that sequence could be:

    (1/5)n^5 - 2n^4 + 11n^3 - (55/2)n^2 + (383/10)n - 9

    • ...Show all comments
    • Pinkgreen
      Lv 7
      1 month agoReport

      It was because you had used the polynomial
      T(n)=an^5+bn^4+cn^3+dn^2+en+f to determine T(n)
      by finding the coefficients of a,b,c,d, e & f.

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