The order is part of it
What makes a list of numbers a sequence?
A sequence is an ordered list of numbers, each one called a term.
↳ There is a first term, a second, a third, and so on.
📚 Chapter Learning Kit
Sequences and Progressions · Class 9 Mathematics
English 3 topics 172 leveled MCQs 60 flashcards 4 games Free
Shared by a Veda teacher · Generated with Veda AI · Oct 2026
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The subscript is a position
How the terms are named.
$t_1$ is the first term, $t_2$ the second, and $t_n$ the $n$th.
↳ Reading $t_n$ as $t \times n$ is the commonest notation slip in the chapter.
No, and that is allowed
Does every sequence have a rule?
The primes $2, 3, 5, 7, 11, \ldots$ form a perfectly good sequence with no simple formula for the $n$th term.
↳ Order is the requirement; regularity is not.
An arithmetic progression
A sequence whose gaps never change.
In $1, 5, 9, 13, 17, \ldots$ the difference between consecutive terms is always 4.
↳ That constant gap is the common difference, $d$; the start is the first term, $a$.
a plus (n minus 1) times d
The rule for the $n$th term of any AP.
$$t_n = a + (n-1)d$$
↳ The number of steps is always one less than the position.
The first term is where you start
Why is it $n - 1$ and not $n$?
You do not step to reach $t_1$; you begin there. Only $t_2$ onwards costs a step.
↳ This is the single most common error in the whole chapter.
📖 Smart notes
What you'll study, topic by topic
1
Sequences, and the Two Ways of Giving a Rule
A sequence is an ordered list of numbers, and predicting what comes next means finding its rule. There are two quite different kinds: one reaches any term straight from its position, the other builds each term from the o…
~40 min · full explanation, examples & memory tricks in the app
2
Arithmetic Progressions, and the Sum of the First n Whole Numbers
A sequence that grows by the same amount every time is called an arithmetic progression, and two numbers describe it completely: where it starts and how big each step is. From those, any term can be reached directly. A s…
~45 min · full explanation, examples & memory tricks in the app
3
Geometric Progressions
A sequence that multiplies by the same amount every time is called a geometric progression, and like an arithmetic one it is described completely by where it starts and what each step does. The difference between adding…
~45 min · full explanation, examples & memory tricks in the app
❓ Leveled MCQ practice
Try the smart MCQs from this kit
172 questions laddered from warm-up to topper-level, each with an explanation. A taste:
A recursive rule for a sequence gives
Beginner
A The $n$th term directly from $n$
B Each term from the term or terms before it
C The sum of all the terms
D The number of terms
Show answer & explanation
Each term from the term or terms before it
And it must name a starting value as well.
Each number in a sequence is called a
Beginner
A Factor
B Root
C Term
D Coefficient
Show answer & explanation
Term
Terms are named by their position, so $t_3$ is the third of them.
In the notation $t_n$, what does the small $n$ stand for?
Beginner
A A number to multiply $t$ by
B The number of terms altogether
C The common difference
D The position of the term in the list
Show answer & explanation
The position of the term in the list
Reading $t_n$ as $t$ times $n$ is the commonest notation slip in the chapter.
Must every sequence follow a simple rule?
Intermediate
A Yes, every sequence has an explicit rule
B Yes, but only recursive rules
C No — the primes have no simple formula for the $n$th term
D Only sequences of whole numbers need a rule
Show answer & explanation
No — the primes have no simple formula for the $n$th term
Order is what makes a list a sequence; regularity is a bonus.
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