Is it a bad idea to use the first book in a series as a reader magnet?

Hi! I’ve written a trilogy (the first 2 books are published already) and I’ve been toying with the idea of using the first book in the series as a reader magnet.

I have a short story that I’ve been using which is related to the series I’ve been writing. However, short stories are not my strength and I feel the first book in the series is a more accurate sample of my writing?

So, is it a good strategy to offer the first book as a reader magnet, or could that cheapen my work in the eyes of my readers?