Homeclass 10MathsArithmetic ProgressionsSequence

Sequence

A sequence is an ordered list of numbers arranged according to a specific mathematical rule or pattern. Each number in the sequence is called a term, and its position determines its value.

Key Concepts

Sequences can be finite, having a specific number of terms, or infinite, continuing indefinitely without an end.
The terms of a sequence are usually denoted by a1, a2, a3, and so on, where the subscript indicates the position of the term.
In the context of arithmetic progressions, a sequence follows a strict rule where the difference between any two consecutive terms is always constant.

Formula & Equation

an = f(n)

an represents the nth term of the sequence, and n is the position of the term which is a positive integer.

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Common Misconceptions

Myth: A sequence and a series are the exact same mathematical concept.
Fact: A sequence is simply an ordered list of numbers, while a series is the sum of the terms of that sequence.

Real World Applications

The arrangement of seats in a stadium where each successive row has a specific number of additional seats.
The amount of money in a piggy bank when a fixed amount is deposited every day.

Frequently Asked Questions

What is the difference between a finite and an infinite sequence?
A finite sequence has a limited number of terms and ends with a last term, whereas an infinite sequence continues forever without a final term.
How do you find the nth term of a sequence?
You can find the nth term by identifying the mathematical pattern or rule governing the sequence and substituting the position number n into that rule.

Keep Learning

Arithmetic ProgressionTerm of an Arithmetic ProgressionFirst Term