Because a paper's first paragraph is often difficult to write, many students have learned a 'first paragraph formula'. According to this formula, you start the first paragraph with a thesis statement or question, add two to four supporting statements, and end the first paragraph with a concluding statement. Because all or nearly all of these first paragraph sentences represent topic sentences from the paper's other paragraphs, the first paragraph acts as a summary or even an abstract.
This kind of summary first paragraph may be useful because it does provide some structure, and some structure is better than no structure. But the summary first paragraph is usually ineffective because it introduces ideas without providing necessary context or background - the reader sees the ideas but doesn't really understand them. Moreover, when the same phrases/ideas appear in paragraph 1 and again in paragraphs 2 - 5, the paper sounds redundant. The sense of redundancy is especially strong with short essays (4 pages or less).
If you are writing a short essay, do not use the first paragraph to summarize. Instead, use the first paragraph to describe the problem or question. And then develop and analyze that problem and question in the following paragraphs. Finish with some conclusion but avoid repeating the points you just made - in a short paper, this repetition will sound redundant and will therefore be ineffective.
If you are writing a longer paper, do not try to introduce everything in the first paragraph. Instead, use three or more paragraphs as an introduction. Each paragraph should provide enough context or background so that that the reader fully understands where the paper is going while he or she is reading that paragraph; in other words, the reader should not have to read paragraph 4 to reasonably understand sentences in paragraph 1.
Here is one common and useful pattern for research papers:
Paragraph 1 describes the problem or question.
Paragraph 2 describes what previous research has revealed.
Paragraph 3 indicates the limitations of this previous research: contradictions, unknowns, poor assumptions, etc.
Paragraph 4 indicates what will be new about the current paper.
Of course, each of these paragraphs may require additional paragraphs, so don't infer that there is some proper number of paragraphs.
Having codified this pattern by writing it down, I now worry that it will produce formulaic and therefore dull introductions. Although that is possible, the diversity and complexity of subject matter should usually color or mask the underlying structure so that the reader pays more attention to the subject matter than to paragraph arrangement. On the other hand, other patterns for introductions could be more effective, and effective writers will enjoy finding them.