This word is acceptable for play in the US & UK dictionaries that are being used in the following games:

• Lexulous
• Wordscraper
• Wordosaur

ad. Without a motive.

"She found it hard to write letters when he was walking about, sometimes watching the point of her pen, lifting a cup and putting it down again, reading a few paragraphs of the paper and dropping it listlessly, opening the cupboard door motivelessly and closing it again, lifting down books, peering behind them and letting them slip from his hands to the floor with a bang."

motiveless