arithmetic and a geometric sequence?

Question

Is there a sequence of rational numbers that is both an arithmetic and a geometric sequence? (Can anyone help?)

rammstein53 · Answer

all followers have the same distance a(n+1) – a(n) = const

all followers have the same ratio a(n+1) / a(n) = const

at the same time, this applies only to a(n) = const for all n

mihisu · Answer

Yes, there are, the constant consequences…

[with any constant c. ε Q]

This is an arithmetic sequence with difference parameters d = 0.
And it is a geometric sequence with growth factor q = 1.

Note: However, there is no non-constant sequence of rational numbers which is at the same time arithmetic sequence and geometric sequence.

uwe65527 · Answer

There is the zero sequence a(n)=0 a(n+1) = a(n) + 0 and a(n+1) = a(n) * 1 And there is the one-follow a(n)=1 a(n+1) = a(n) + 0 and a(n+1) = a(n) * 1