1. Introduction: Patterns That Grow by the Same Step
Look around your day. The world is full of lists of numbers that climb or fall in a steady way.
Picture a ladder leaning against a wall. The rungs are evenly spaced. From the ground, the first rung is at 30 cm, the next at 55 cm, the next at 80 cm. Each rung sits 25 cm above the one below it. Same gap, every time.
Or think of a worker whose pay starts at 8000 rupees a month. Each year the boss adds 500 rupees. So the monthly pay goes 8000, 8500, 9000, 9500, and on. The jump is 500 every year. Same jump, every time.
Or a child saving in a clay piggy bank. On day one she drops in 5 rupees. Each day after, she adds 5 more than nothing extra — she just keeps adding 5. So the box holds 5, 10, 15, 20 rupees as the days pass.
Stop scrolling. Try it in your head before reading on. In the ladder list — 30, 55, 80 — what comes next?
If you said 105, you already feel the idea. You did not guess. You spotted that each step adds the same amount, and you used it to predict.
A sequence is just a list of numbers written in a fixed order. Each number in it is called a term. The lists above are special sequences: they grow by adding the same fixed amount each time. That is the whole topic of this lesson.
You can now sense what we are chasing: lists of numbers that move by a fixed step.