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

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

3. The last term of an infinite sequence

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

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

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

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

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

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

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

11. A sequence is also known as

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

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

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

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

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

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

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

19. The sum of terms of a sequence is called

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

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