Tag: Sequence

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

 20

 3

 14

 5

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

 10

 11

 None of These

 9

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

 Natural Numbers

 Integers (Z)

 Real Number

 Rational Numbers (Q)

4. The last term of an infinite sequence

 is nth term

 Does not exist

 is $a_n$

 is general term

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

 $3n+5$

 $3n-13$

 $3n-9$

 $3n-5$

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

 660

 110

 6

 24

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

 H.P.

 None of These

 G.P.

 A.P.

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

 Combination

 Permutation

 Series

 Sequence

9. A sequence is also known as

 Complex Sequence

 Real Sequence

 Arrangement

 Progression

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

 Cannot be Determined

 29

 12

 9

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

 Real Sequence

 Complex Sequence

 Natural Sequence

 Imaginary Sequence

12. The sum of terms of a sequence is called

 Finite Sum

 Series

 Partial Sum

 None of These

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

 $\frac{c+d}{2cd}$

 $\frac{c+d}{2}$

 $\frac{2}{c+d}$

 $\frac{2cd}{c+d}$

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

 124

 120

 None of These

 112

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

 $\frac{a_{n-1}+a_{n+1}}{2}$

 $\frac{a_{n+1}-a_{n-1}}{2}$

 $a_{n+1} – a_{n-1}$

 $\frac{a_{n-1}-a_{n+1}}{2}$

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

 $a_n=a-(n+1)d$

 $a_n=a+(n+1)d$

 $a_n=a-(n-1)d$

 $a_n=a+(n-1)d$

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

 16

 1 + 4 + 9 + 16

 8

 1 + 2 + 3 + 4

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

 $\left(\frac{2n+1}{3}\right)^2$

 $\left(\frac{2n}{3}\right)^2$

 Cannot be Determined

 $\left(\frac{2n-1}{3}\right)^2$

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

 $5-6n_2n^2$

 $5-6n+4n^2$

 $5-6n+8n^2$

 $5+6n+4n^2$

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

 $\frac{4}{\sqrt{2}}$

 $4\sqrt{2}$

 None of These

 $\sqrt{2}$

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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 $a_n=\frac{1}{a_1+(n-1)d}$

An online quiz about Computer