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 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.