Can Geometric Progressions Starting from One Sum to a Perfect Square?

[Medtner]

"Write out a series of three or more different whole numbers in geometric progression, starting from one, so that the numbers should add up to a square. So like, 1 + 2 + 4 + 8 + 16 + 32 = 63 (one short of a square)"(can't find an actual real life example)

I can't seem to find an answer for this?

 

[mfb]

Just use a spreadsheet to try some more, there are two three-digit examples.

 

[fresh_42]

Here you can find the formulas:

https://en.wikipedia.org/wiki/Geometric_progression

 

[MAGNIBORO]

1+3+9+27+81=121=11^2

 

[thefurlong]

"Write out a series of three or more different whole numbers in geometric progression, starting from one, so that the numbers should add up to a square. So like, 1 + 2 + 4 + 8 + 16 + 32 = 63 (one short of a square)"(can't find an actual real life example)

I can't seem to find an answer for this?

Try considering the sequence of squares, 0, 1, 4, 9, ..., and take the difference between subsequent squares. That will help you find the answer.