SEQUENCES AND SERIES
Frequently Asked Questions
A sequence is an ordered list of numbers written according to a definite rule, where each number is called a term of the sequence.
In a sequence, order matters and repetition is allowed, whereas in a set order does not matter and repetition is not allowed.
The nth term is the general term of a sequence that represents the term at position \(n\).
A finite sequence has a limited number of terms, such as \(2,4,6,8\).
An infinite sequence has infinitely many terms, such as \(1,2,3,\dots\).
A series is the sum of the terms of a sequence.
A sequence lists terms, while a series represents their sum.
An arithmetic progression is a sequence in which the difference between consecutive terms is constant.
The common difference \(d\) is the difference between any term and its preceding term.
The general form of an AP is \(a, a+d, a+2d, a+3d, \dots\).
The nth term of an AP is given by \(a_n = a + (n-1)d\).
The symbol \(a\) represents the first term of the arithmetic progression.
The common difference is found by dividing the difference of the terms by the difference of their positions.
An arithmetic mean is a number inserted between two numbers such that all three form an AP.
The arithmetic mean is \(\dfrac{a+b}{2}\).