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What is the 20th term of the arithmetic sequence 4, –2, –8, … ? –110 –116 –122 –128 What is the sum of a 17–term arithmetic sequence where the first term is 9 ...show more
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1).
What is the 20th term of the arithmetic sequence 4, –2, –8, … ?
–110

2).
What is the sum of a 17–term arithmetic sequence
where the first term is 9 and the last term is –87?
Difference = 96/17
5< D < 6
9 + 4 + (-1) + (-6) + ...... +(-71)-----> -527
9 + 3 + (-3) + (-9) + ...... +(-87)------) -663

–663

3).
The 17th term of the arithmetic sequence 17, 21, 25, … ?
81
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  • John G answered 3 years ago
    1. Looks like it follows the equation 10-6n where n is the number of the term
    thus the 20th term is 10-6(20) or 10-120 = -110

    2. Let the equation be A+nB
    the first term is A+B = 9
    the 17th term is A+17B=-87

    equation 2 less equation 1 is 16B = -96..........B = -6 .......A = 15

    so the 17-term sequence starts with 15-6(1)...15-6(2)......to 15-6(17)

    the sum is 15(17)-6(sum 1 to 17)........................sum (1-17) is 17(17+1)/2 = 153

    thus 15(17) -6(153)
    = 255 - 918
    = -663


    3. looks like the formula there is 13 + 4n
    so the 17th term is 13 + 4(17)
    = 13 + 68
    = 81
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  • Chandreyee C answered 3 years ago
    the last one is 85
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  • Laughaholic :D answered 3 years ago
    1) -110
    2)-718
    3) 79

    Source(s):

    pre-algebra student [;
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  • Kiki answered 3 years ago
    You are using the equation An= A1 + (n-1)d
    1) A1= 4(first number) n= 20( number of term you want) d= -6 ( you are taking away 6 to get to each new term)
    Now just plug in and solve:
    An= 4 + (20-1)(-6)
    Answer: -110

    Now use the equation Sn= n/2(An+A1)
    2) n=17 An=-87 A1=9
    Plug in and solve:
    Sn= (17/2)(-87 + 9)
    Answer: -663

    Use An= A1 + (n-1)d again
    3) n=17 A1=17 d=+4
    Plug in and solve:
    An= 17 + (17-1)(4)
    Answer: 81

    Source(s):

    Math Teacher
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