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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 $B?$ \begin{itemize} \item Sequence $A:$ $2,$ $4,$ $8,$ $16,$ $32,$ $\ldots$ \item Sequence $B:$ $20,$ $40,$ $60,$ $80,$ $100,$ $\ldots$ \end{itemize}

 Jan 25, 2015

Best Answer 

 #1
avatar+130540 
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Here's A

2,  4,  8,  16,  32, 64, 128,   256,    512

Here's B

20,40,60,80,100,120,140,160,180,200,220,240,260,280, 300, 320

The least positive difference appears to be 4...this occurs three times

20 - 16,  64-60    and    260-256

 

 Jan 25, 2015

1+0 Answers

 #1
avatar+130540 
+5
Best Answer

Here's A

2,  4,  8,  16,  32, 64, 128,   256,    512

Here's B

20,40,60,80,100,120,140,160,180,200,220,240,260,280, 300, 320

The least positive difference appears to be 4...this occurs three times

20 - 16,  64-60    and    260-256

 

CPhill Jan 25, 2015

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