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

$\displaystyle a=81$ --- 1

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

Solve for d (common difference) , then add it to the first term and every subsequent term .

hi

$\displaystyle a=81$ --- 1

$\displaystyle T_6=954\Rightarrow a+5d=954$ ---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 $\displaystyle d$

4. Originally Posted by HNCMATHS
Hello Mathaddict, please could you explain how to work out the value of $\displaystyle d$
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:. . $\displaystyle 81\; \underbrace{\qquad}_d\; ? \; \underbrace{\qquad}_d \; ? \; \underbrace{\qquad}_d \; ? \; \underbrace{\qquad}_d \;? \; \underbrace{\qquad}_d \; 954$

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

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

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

6. Originally Posted by Soroban
Hello, HNCMATHS!

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

We have six equally-spaced numbers:. . $\displaystyle 81\; \underbrace{\qquad}_d\; ? \; \underbrace{\qquad}_d \; ? \; \underbrace{\qquad}_d \; ? \; \underbrace{\qquad}_d \;? \; \underbrace{\qquad}_d \; 954$

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

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

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