Too white to tan?

I have pretty pale skin with red undertones...so what I am wondering is if I am to white to tan? I have tanned a tiny tiny but in the past but I was wondering if I kept trying would I eventually get some color.
Too white to tan?
I am really white and I was with some girls who were goin tanning and i had no where to go so they went in and i went in and they were already gone so I was like well I'll have a 20 minute regular tan. I didn't burn bad and it wasn't painful, just remember to make sure you aren't laying on anything -_-