What is the next number in the sequence?

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SUMMARY

The sequence 2, 2, 8, 72, 392, 2312 represents the areas of rectangles with a 2:1 ratio, where each number corresponds to the area of successively larger rectangles. The next number in the sequence can be derived by identifying the pattern in the areas based on the dimensions of the rectangles. The discussion emphasizes the geometric representation of the sequence and the mathematical relationship between the dimensions of the rectangles.

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2, 2, 8, 72, 392, 2312, ?

The sequence can be represented visually by the attached image.

The smallest rectangles are 2x1. Every rectangle has a 2:1 ratio. Each number in the sequence represents the area of each successively larger rectangle.

I can figure out the next number, but I can't figure out how to represent it mathematically.
 

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  • SequenceHuh.jpg
    SequenceHuh.jpg
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Welcome to PF aykantspel.

Suppose that you have somewhere a rectangle with sides of length L and 2L. Possibly looking at the picture, can you say in terms of L what the sides of the next bigger rectangle will be?

You can start by drawing an example: if L = 1 you start with a 2 x 1 rectangle, what will be the size of the next?
 

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