:) I'm new here and I have a question for which I didn't find any hint on the website, yet. Maybe you can help me :).
I am trying to find out whether geometric progressions with real entries are R-vector spaces.
I found the solution for an arithmetic progression, but now for geometric ones I struggle to see it intuitively, especially on the closure under addition statement. I.E is the sum of two geometric progressions also a GP ?
$a_{n+1}=r\cdot a_{n}$ , $b_{n+1}=r\cdot b_{n} \\$
$(a+b)_{n+1}=(a+b)_{n}\cdot r $
Thank you very much in advance :)