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Math Help - Arithmetic Progression

  1. #1
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    Question Arithmetic Progression

    Afternoon All.

    Another question from my practise test paper... (Not really sure how to go about this one)

    A lathe has a range of six speeds. the lowest beign 81 RPM and the highest beign 954 RPM. Determine the six speeds if they are arranged in arithmetic progression.

    Thanks in advance for any help
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  2. #2
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    Quote Originally Posted by HNCMATHS View Post
    Afternoon All.

    Another question from my practise test paper... (Not really sure how to go about this one)

    A lathe has a range of six speeds. the lowest beign 81 RPM and the highest beign 954 RPM. Determine the six speeds if they are arranged in arithmetic progression.

    Thanks in advance for any help
    hi

    a=81 --- 1

    T_6=954\Rightarrow a+5d=954 ---2

    Solve for d (common difference) , then add it to the first term and every subsequent term .
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  3. #3
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    Quote Originally Posted by mathaddict View Post
    hi

    a=81 --- 1

    T_6=954\Rightarrow a+5d=954 ---2

    Solve for d (common difference) , then add it to the first term and every subsequent term .
    Hello Mathaddict, please could you explain how to work out the value of d
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  4. #4
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    Quote Originally Posted by HNCMATHS View Post
    Hello Mathaddict, please could you explain how to work out the value of d
    a=81 , a+5d=954 so 81+5d=954 ....
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  5. #5
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    Hello, HNCMATHS!

    A lathe has a range of six speeds.
    The lowest begins at 81 RPM and the highest begins at 954 RPM.
    Determine the six speeds if they are arranged in arithmetic progression.
    We don't need any fancy formulas, do we?


    We have six equally-spaced numbers:. . <br />
81\; \underbrace{\qquad}_d\; ? \; \underbrace{\qquad}_d \; ? \; \underbrace{\qquad}_d \; ? \; \underbrace{\qquad}_d \;? \; \underbrace{\qquad}_d \; 954

    The range is: . 954-81 \:=\:873

    So the numbers are spaced: . d\:=\:\tfrac{873}{5} \,=\,174.6 apart.


    The six speeds are: . 81,\;255.6,\;439.2,\;604.8,\;779.4,\;954
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  6. #6
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    Quote Originally Posted by Soroban View Post
    Hello, HNCMATHS!

    We don't need any fancy formulas, do we?


    We have six equally-spaced numbers:. . 81\; \underbrace{\qquad}_d\; ? \; \underbrace{\qquad}_d \; ? \; \underbrace{\qquad}_d \; ? \; \underbrace{\qquad}_d \;? \; \underbrace{\qquad}_d \; 954 " alt="
    81\; \underbrace{\qquad}_d\; ? \; \underbrace{\qquad}_d \; ? \; \underbrace{\qquad}_d \; ? \; \underbrace{\qquad}_d \;? \; \underbrace{\qquad}_d \; 954 " />

    The range is: . 954-81 \:=\:873

    So the numbers are spaced: . d\:=\:\tfrac{873}{5} \,=\,174.6 apart.


    The six speeds are: . 81,\;255.6,\;439.2,\;604.8,\;779.4,\;954
    Spot on, Thank you very much
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