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i am stuck on this one math problem. The question is to write a rule for the pattern (it is a section on sequences)
The pattern is -5,10,-15,20,-25. What is the rule? A sub n = ?

  • Algebra -

    termn = (5n)(-1)^n

  • Algebra -

    The signs are alternating and each term is
    a multiple of 5. The rule would be

    (-1)^n(5*n) where n are the integers
    1 through 5. To show you that this is true I will evaluate the expression for
    each value of n 1 through 5

    n=1 (-1)^1*5*1=-1(5)=-5

    n=2 (-1)^2*5*2=1(10)=10

    n=3 (-1)^3*5*3=-1(15)=-15

    n=4 (-1)^4*5*4=1(20)=20

    n=5 (-1)^5*5*5=-1(25)=-25

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