The Draft blog for NYTimes had a great article on the effectiveness of the short sentence. In Scholarly Writing, I try to reiterate that shorter sentences help with clarity. The longer the sentence, the more likely the reader is to get lost in the words and lose the overall idea. As a guideline, about 20 - 25 words per sentence is ideal and even shorter sentences may be more effective.
As the article on the blog notes, you should "[e]xpress your most powerful thought in the shortest sentence. Writers can use it to give even preposterous statements the ring of truth. The bigot can use it to foment hate. The propagandist can slap it on a bumper sticker. But for the writer with good intent, the short sentence proves a reliable method for delivering the practical truth. With punch."
Additionally, "[u]sing short sentences to their full effect is a centuries-old strategy, found in opinion writing, fiction and nonfiction, poetry and plays. It works in a formal speech or in a handwritten letter. Shakespeare had a messenger deliver the news to Macbeth in six words: 'The Queen, my lord, is dead,' a message that could fit easily inside a 140-character tweet."
As you can see, those five words, "The Queen, my lord, is dead," is all that needs to be said. It's effective and maintains the seriousness of the message.
"A long sequence of short sentences slows the reader down, each period acting as a stop sign. That slow pace can bring clarity, create suspense or magnify emotion, but can soon become tedious. It turns out that the short sentence gains power from its proximity to longer sentences [so don't be afraid to use longer sentences]. A familiar and effective place for the [very] short sentence is at the end of a long paragraph."
To really add oomph to an idea, you should consider trying to convey your thought in a five word sentence at the end of a paragraph. It will leave the reader with a lasting impression.