maths problem

[irelandscall]

a milling machine must accomodate work between 50 mm and 300 mm.To complete this task 8 speeds are required.
If the 1st speed is 27m/min and the 8th speed is 420m/min find using geometric progression the 8 speeds and list the sequence of speeds to the nearest full revolution.
What are the workings for this problem please??

[Fibonacci]

A geometric progression is one on which each term is multiplied by a constant value to get the next term
General form of a G. P.: a, ar, ar^2, ar^3, ...

The first term of your progression (a) = 8 and the eight term (ar^7) = 420
so ar^7 / a = r^7 = 420/8 = 52.5
so now you know r^7 is 52,5

now solve the equation r^7 = 52,5 and you have found the constant value and can then find the missing terms by multiplying each term starting from 8 by this result.

( n.b. ^ is an accepted way of typing to the power of)

[factor-fiction]

ibonnacci's answer is realy helpful except I think the first term is 27 not 8 , so the first 8 terms are (to 2 decimal places):
27.00
39.96
59.14
87.53
129.55
191.74
283.78
420.00

[Fibonacci]

quite right factor 30 - don't know where 8 came form the equation needing to be solved is r^7 = 420/27 = 15.55555....

[factor-fiction]

Irelandscall- the best way to solve this is using the formula Fibonacci used for the Geometric Progression, but an alternative is simply to use a spreadsheet and by trial error you can try different values of r until you get one that gives the right answer

[factor-fiction]

Well, was this helpful? Was all our hard work worthwhile?