algebra

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I have 3 questions I need help with.
1) what is the 15th term of the sequence 81,27,9,...

2) what is a possible value for the missing term of the geometric sequence 39,_,975,_

3) what is the sum of the finite arithmetic series (-5)+0+5+10+..+65

  • algebra -

    your first sequence looks geometric with
    a = 81, r = 1/3

    term(15) = ar^14
    = 81(1/4782969)
    = 1/59049

    2. let the missing term be x
    then x/39 = 975/x
    x^2 = 38025
    x = ± √38025 = ± 195
    could be 195 or -195

    3. looks arithmetic with a = -5 , d = 5
    term(n) = 65
    -5 + (n-1)(5) = 65
    5n - 5 = 70
    5n = 75
    so we have 15 terms

    sum(15) = (15/2)(first + last)
    = 15/2(-5+65) = 450

  • algebra -

    the first and second is not a possible answer.
    1) 1/729
    1/243
    1/81
    1/810

  • algebra -

    1. proof that my answer is correct

    81 27 9 3 1 1/3 1/9 1/27 1/81 1/243 1/729 1/2187 1/6561 1/19683 1/59049
    count the terms

    2. proof my answer is correct:
    195/39 = 5
    975/195 = 5

    -195/39 - -5
    975/-195 = -5

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