Lesson 1 of 10 · 7 min

What a sequence is

NCERT §8.1, §8.2

Meera has two savings jars. Into the first she puts ₹100 in week 1 and ₹50 more each week after that. Into the second she puts ₹1 in week 1 and doubles it every week. She writes each week's amounts in two columns in a notebook. Which column is the more useful list to understand?

The story this chapter follows: Meera's two savings jars

Imagine Meera, who keeps two savings jars. Jar A starts with ₹100 and gets ₹50 more each week than the week before; jar B starts with ₹1 and doubles each week. One grows by adding, the other by multiplying. Which jar holds more, and when does that change? The amounts are made up for easy arithmetic, and they carry most of the examples in this chapter.

The lesson in notes

In short

A sequence is a list of numbers in a definite order: there is a first term, a second term, a third term and so on. The terms are written a₁, a₂, a₃, …, and aₙ, the term in position n, is called the nth or general term.

Ancestors give an example. With a gap of 30 years between generations, 300 years covers 300/30 = 10 generations, and the numbers of ancestors in them are 2, 4, 8, 16, …, 1024. Here a₁ = 2 and a₁₀ = 1024.

Dividing 10 by 3 step by step gives the quotients 3, 3.3, 3.33, 3.333, …, which never end.

A sequence with a fixed, countable number of terms is finite (the 10 generations of ancestors). One that never ends is infinite (the quotients of 10 ÷ 3).

Sequences whose terms follow a definite pattern are called progressions.