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Question:

sophiaa
sophiaa
Student
High School - 9th Grade

Arithmetic progression. I have to find out the first term and the ratio! We know the third term = 8 and the seventh term of progression= 20.

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Posted by sophiaa on Saturday January 31, 2009 at 10:58 AM and tagged with first term, math, progression, ratio.

Answers:

  1. giorgiana1976
    giorgiana1976 Teacher
    Doctorate

    Best answer as selected by question asker.

    We know the formula for any term of an arithmetic progression:

    an=a1 + (n-1)r, where a1 is the first term and r is the ratio.

    a3=a1 + (3-1)r

    a7=a1 + (7-1)r

    Doing the substitution where we know the values

    8 = a1 + 2r

    20 = a1 + 6r

    We are subtracting the second relation from the first one and the result will be

    8-20 = a1 + 2r -a1 - 6r

    -12 = -4r

    r=3

    With the known value of r, we go back in the first relation and making substitution of r

    8 = a1 + 2r

    8 = a1 + 2x3

    8 = a1 + 6

    a1= 8-6

    a1=2

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    Posted by giorgiana1976 on Saturday January 31, 2009 at 11:05 AM