This post is about all the Online Quizzes related to Sequence and Series from the Mathematics Book of Part I (First Year). Click the links below to start with Online MCQs Sequence and Series Quizzes.
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A sequence is an ordered set of numbers formed according to some definite rule. A sequence can be defined as a function whose domain is a subset of natural numbers. Mathematically, a sequence is denoted by $\{a_n\}$ where $n\in N$.
Some examples of sequence are:
- $1,2,3,\cdots$
- $2, 4, 6, 8, \cdots$
- $\frac{1}{3}, \frac{1}{5}, \frac{1}{7}, \cdots$
The term $a_n$ is called the general term or $n$th term of a sequence. If all numbers of a sequence are real, then it is called a real sequence. If the domain of a sequence is a finite set, then the sequence is finite otherwise the sequence is infinite. An infinite sequence has no last term.
If the terms of a sequence follow a certain pattern, then it is called a progression:
- Arithmetic Progression (AP)
A sequence $\{a_n\}$ is an Arithmetic Sequence or Arithmetic Progression if the difference $a_n – a_{n-1}$ is the same for all $n \in N$ and $n>1$. - Geometric Progression (GP)
A sequence $\{a_n\}$ in which $\frac{a_n}{a_{n-1}}$ is same non-zero number for al l$n\in N$ and $n>1$ is called Geometric Sequence or Geometric Progression. - Harmonic Progression (HP)
A Harmonic Progression is a sequence of numbers whose reciprocals form an Arithmetic Progression. A general form of Harmonic Progression is $\frac{1}{a_1}, \frac{1}{a_1+d}, \frac{1}{a_1+2d}, \cdots$, where $a_n=\frac{1}{a_1+(n-1)d}$
Try MCQs Multivariate Analysis