1. ## Arithmetic Progression

Afternoon All.

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

2. Originally Posted by HNCMATHS
Afternoon All.

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 .

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 $d$

4. Originally Posted by HNCMATHS
Hello Mathaddict, please could you explain how to work out the value of $d$
a=81 , a+5d=954 so 81+5d=954 ....

5. 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:. . $

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

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

The six speeds are: . $81,\;255.6,\;439.2,\;604.8,\;779.4,\;954$

6. Originally Posted by Soroban
Hello, HNCMATHS!

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

We have six equally-spaced numbers:. . $

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