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An arithmetic progression is $a+0b, a+1b, a+2b, ..., a+nb$

A geometric progression is $ab^0, ab^1, ab^2, ..., ab^n$.

Multiplication is arithmetic, so why is a geometric progression not also an "arithmetic" progression?

A line being extended be iteratively adding a constant length is a geometric construction, so why is an arithmetic progression not also a "geometric" progression?

Martin Sleziak
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spraff
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  • It appears to be an exact duplicate of Q820680 on math. It's really not a question of the Use of English. – Andrew Leach Jan 23 '21 at 09:36
  • Because there's a very nice geometric visualization, I suppose. This one is for $a=1$ and $b=\frac{1}{2}$ specifically: https://images.hive.blog/p/JvFFVmatwWHVQPjDcGkFxELgGtwNAntRtiqDuEyy8Rghsyf7R2YFZ82HfFY76VyvBMgXavpaUh2DcFSWCA3S1euK7XxZRas1jCPxUek9TxQb822EeHgUB39jErdxPsoTjNX2oczCyL?format=match&mode=fit&width=768 – Vercassivelaunos Jan 23 '21 at 09:41
  • link to the above mentioned question and do look at the linked questions therein. – V.G Jan 23 '21 at 09:42
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    None of the linked answers are satisfactory. This is an excellent question. – John Douma Jan 23 '21 at 10:37
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    This has been migrated once already, but likely a better place to ask is on the History of Science & Mathematics forum. I agree with John Douma that the interpretations of geometric series by geometry (while nice) do not address why they were originally given these names. But C. Oliveira's post on the linked question does provide some good research on the matter. – Paul Sinclair Jan 24 '21 at 01:17

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