Six speeds

A drilling machine is to have 6 speed ranging from 50 to 750 revolution per minute. If the speed forms a geometric progression, determine their values.

Correct result:

a1 =  50 rpm
a2 =  85.9386 rpm
a3 =  147.7088 rpm
a4 =  253.8778 rpm
a5 =  436.3581 rpm
a6 =  750 rpm

Solution:

a1=50=50 rpm
a6=750 rpm  a6=q5 a1  q=a6/a15=750/505≐1.7188   a2=q⋅ a1=1.7188⋅ 50=85.9386 rpm
a3=q⋅ a2=1.7188⋅ 85.9386=147.7088 rpm
a4=q⋅ a3=1.7188⋅ 147.7088=253.8778 rpm
a5=q⋅ a4=1.7188⋅ 253.8778=436.3581 rpm
a6=q⋅ a5=1.7188⋅ 436.3581=750 rpm

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