Question 639363: Solve for the next two numbers in the following number sequence: 1728, 1000, 512, 216, _, _.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Each number is a perfect cube. Notice how 12^3 = 1728, 1000 = 10^3, 512 = 8^3, 216 = 6^3
So the form is n^3 where 'n' is some integer. But we're only focusing on positive even integers and we're counting down to the next even integer each time. Moreover, we're starting at 12. So 'n' becomes -2n+12 where n starts at n = 0. If you want to start at n = 1, then you have to add 2 to 12 to get -2n+14
So the sequence follows the form (-2n+14)^3 where n is a positive integer and n starts at n = 1
We can see that when n = 1, (-2n+14)^3 = (-2*1+14)^3 = 1728
When n = 2, (-2n+14)^3 = (-2*2+14)^3 = 1000
etc etc
all the way up to n = 4, (-2n+14)^3 = (-2*4+14)^3 = 216
The next two terms are
n = 5, (-2n+14)^3 = (-2*5+14)^3 = 64
and
n = 6, (-2n+14)^3 = (-2*6+14)^3 = 8
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Answer:
So the updated sequence is
1728, 1000, 512, 216, _64_, _8_
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