Category: Sequence & Series

Sequence and Series-2

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

1. Which of the following cannot be the term of sequence 17, 13, 9, …

 
 
 
 

2. The symbol used to represent the sequence $a$ is

 
 
 
 

3. The A.M. between $1-x+x^2$ and $1+x-x^2$ is

 
 
 
 

4. The $n$th A.M. between $a$ and $b$ is

 
 
 
 

5. If $a_{n-2}=3n-11$ then $n$th term will be

 
 
 
 

6. Sequence is also called

 
 
 
 

7. If 5, 8 are two A.M. between $a$ and $b$ then $a$ and $b$ are

 
 
 
 

8. If the domain of a sequence is finite then the sequence is called

 
 
 
 

9. If in an A.P. $a_5=13$ and $a_17=49$, then $a_15=?$

 
 
 
 

10. The number of terms of the series $-7+(-5)+(-3)+\cdots$ amount to 65

 
 
 
 

11. The arithmetic mean between 2+\sqrt{2}$ and $2-\sqrt{2}$ is

 
 
 
 

12. Find the number of terms in an A.P. in which $a=3, d=7$, and $a_n=59$

 
 
 
 

13. The sequence $1, \frac{3}{2}, \frac{5}{4}, \frac{7}{8}, \cdots $, then $a_7=?$

 
 
 
 

14. A sequence in which every term after the first can be obtained by adding a fixed number in the preceding term is called

 
 
 
 

15. If $S_2, S_3, S_5$ are the sums of $2n, 3n, 5n$ terms of an A.P. then which one is true

 
 
 
 

16. If $\frac{1}{a}, \frac{1}{b}$ and D\frac{1}{c}$ are in A.P. then which one is true:

 
 
 
 

17. If all the members of a sequence are real numbers then the sequence is called

 
 
 
 

18. The sum of the series $-3+(-1)+(1) +3+5 +\cdots+ a_{16}$ is

 
 
 
 

19. A sequence is a function whose domain is

 
 
 
 

20. The generl term $a_n$ of an A.P. 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

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.

Please go to Sequence and Series-1 to view the test

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