Tag: Sequence

Sequence and Series-1

This post is about an Online Quiz of sequence and series:

A sequence is an ordered set of numbers formed according to some definite rule.

MCQs about Sequence and Series for the preparation of mathematics

1. An arrangement of numbers according to some definite rule is called

 
 
 
 

2. If $n$th term of an A.P. is $3n-1$ then 10th term is

 
 
 
 

3. If $a_n-a_n-1=n+1$ and $a_4=14$ then $a_5=$?

 
 
 
 

4. The sum of terms of a sequence is called

 
 
 
 

5. If $a_n=\{n+(-1)^n\}$, then $a_{10}$

 
 
 
 

6. A sequence is also known as

 
 
 
 

7. Forth partial sum of the sequence $\{n^2\}$ is

 
 
 
 

8. $n$th term of the series $\left(\frac{1}{3}\right)+ \left(\frac{5}{3}\right)^2+\left(\frac{7}{3}\right)^2+\cdots$

 
 
 
 

9. A sequence is a function whose domain is set of

 
 
 
 

10. A sequence whose range is R i.e. set of real numbers, is called

 
 
 
 

11. The Arithmetic mean between $\sqrt{2}$ and $3\sqrt{2}$ is

 
 
 
 

12. If $a_{n-1}, a_n, a_{n+1}$ are in A.P. then $a_n=$?

 
 
 
 

13. The general term of an A.P. is

 
 
 
 

14. The next term of the sequence $1, 2, 12, 40, \cdots$ is

 
 
 
 

15. The last term of an infinite sequence

 
 
 
 

16. If $a_n=5-3n+2n^2$, then $a_{2n}=$?

 
 
 
 

17. A sequence $\{a_n\}$ in which $a_n-a_n$ is the same number for all $n \in N$, $n>1$, is called

 
 
 
 

18. If $a_{n-2}=3n-11$, then $a_4=$?

 
 
 
 

19. If $a_n=n\,a_{n-1}$, $a_1=1$ then $a_4=$?

 
 
 
 

20. Arithmetic mean between $c$ and $d$ is

 
 
 
 

A sequence can be defined as a function whose domain is a subset of natural numbers. Mathematically, sequence is denoted by $\{a_n\}$ where $n\in N$.

Let us try an Online Quiz about sequence and series:

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 numbers 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 an infinite sequence. 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 $a_n=\frac{1}{a_1+(n-1)d}$
Sequence and Series

An online quiz about Computer