Names of sequence progressions.

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The discussion centers on the mathematical progression defined by Un+1 = KUn + d, exploring its classification. It is noted that this can be reformulated into a recognizable form related to geometric progressions. The conversation highlights the relationship between arithmetic and geometric progressions while seeking a specific name for the new progression type. The participants express gratitude for clarifying the mathematical transformation. The thread concludes without a definitive name for this progression but emphasizes its connection to existing types.
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If Un+1=Un + d defines an arithmetic progression, and Un+1 = kUn defines a geometric progression, is there a name for a progression defined by Un+1 =KUn + d? Thanks.
 
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Hi Aeneas! :smile:

We can rewrite that as Un+1 - d/(1 - K) =K(Un - d/(1 - k)) …

geometric. :wink:
 
Many thanks tiny-tim!
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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