Q.Find the first three terms of the arithmetic progressions whose $n$th term is given. Also find the common difference and the 20th term in each case.

Definition 1: The First Brick in the Wall

Every subject builds itself from definitions. Definition 1 is almost always the most fundamental idea — the one you cannot skip, because everything else rests on it. So let's treat it with the respect it deserves.

The Intuition First

Imagine you are learning a new game. Before you can talk about strategy, scoring, or winning, you need to know what the pieces are and what they do. That is exactly what Definition 1 does: it names the basic object or relation that the entire chapter will play with.

Think of it as the first word in a new language. Without it, you cannot form a sentence. With it, you can start to describe the world.

The Precise Statement

Here is where we need to be careful. You have not told me what subject or chapter this is from. Definition 1 could be anything — the definition of a limit in calculus, a vector in physics, a set in mathematics, a cell in biology, or a force in mechanics.

If you tell me the subject and chapter, I will give you:

• The exact statement, word for word as it appears in standard Indian textbooks.
• The intuition behind each part of the statement.
• A concrete example that makes it stick.
• The common mistake students make with it.

What to Do Right Now …