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Sequence A is a geometric sequence. Sequence B is an arithmetic sequence. Each sequence stops as soon as one of its terms is greater than 300. What is the least positive difference between a number selected from sequence A and a number selected from sequence B? 

 

Sequence A: 2, 4, 8, 16, 32, ...

 

Sequence B: 20, 40, 60, 80, 100, ...

Lightning  Sep 3, 2018
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Why are you having difficulty with this?

 

First thing you should do is to expand the terms of each sequence until you exceed 300!!

 

Sequence A: 2, 4, 8, 16, 32, 64, 128, 256, 512.......etc.

Sequence B: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240, 260, 280, 300, 320.....etc.

 

Then, start with the first term of sequence A, which is 2. Can you subtract it from ANY term of sequence B and get a POSITIVE DIFFERENCE? Obviously not!. How about the 2nd term, which is 4? The same thing applies to the second term. Try the 3rd term which is 8. Same thing! 16 same thing! Now, we get to 32. Obviously you can subtract 32 from the smallest term in sequence B, which happens to be the first term which is 20. So, 32 - 20 =12. But is it the LEAST POSITIVE DIFFERENCE? Well, you can find out by checking the rest of the terms. The next is 64. Now you can subtract it as follows: 64 - 20 =44, 64 -40 =24, 64 -60 =4, which appears to be the LEAST POSITIVE DIFFERENCE!!!

If you try the next term which is 128 and subtract it from the first 6 terms of sequence B, you will get a positive difference greater than 4. The same applies to 256. And that is all.

Guest Sep 3, 2018

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