Some final tips about writing legitimate paragraphs.

Remember that a paragraph consists of a group of related sentences, arranged logically to develop one main idea. Every paragraph needs to include a topic sentence to provide an outline of the paragraph's main idea. Paragraphs also may include transition sentences, supporting sentences and concluding sentences.

Paragraphs dealing with separate aspects of a topic should not be written so that they look like completely independent pieces of writing. Each should be linked with the paragraphs before and after so that there is a clearly developed line of argument through all the paragraphs.
See Logical flow between paragraphs

Paragraphs need to be focussed on one main issue. Therefore all the sentences need to be relevant to that main issue.
See Logical flow within paragraphs

Focused paragraphs can be achieved by having sentences that logically progress.
See Logically flowing sentences