Dear Miss Snark:
I have a friend who insists that it's worthwhile writing the second book in a mystery series before you've sold (or interested an agent in) the first. She says that if she can't find an agent for the first book, she'll start querying about the second book and then tell any interested agents that the first book exists.
This doesn't make sense to me. It seems highly unlikely that an agent would want to pick up the second book in a series if no one wanted the first. My question is this: How would you respond to a query that says, "This is the second book in an as-yet-unpublished mystery series?"
I laugh merrily. It usually means they haven't written enough yet, not too much. Most good writers have a tome or three under the bed before they get an agent interested. They might be standalones, they might be parts of a series; what they universally are is pretty terrible.
I assume the book you're sending me will need to stand alone. That's how I read it at the query stage or the full novel stage.
And, if you're not getting better with each book you write, you've got a problem. Once you have written the third, fourth or fifth book, you're going to look at the first book and cringe. You won't want Miss Snark to get even a whiff of it, let alone try to sell it.
One of the most reliable indices of "not right for me" is "this is my first book, fresh off the printer".
Write a lot. Write ten books in a series if you will. Send me the best, it's probably the last one.