# 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.

1. The arithmetic mean between 2+\sqrt{2}$and$2-\sqrt{2}$is 2. A sequence is a function whose domain is 3. A sequence in which every term after the first can be obtained by adding a fixed number in the preceding term is called 4. The sequence$1, \frac{3}{2}, \frac{5}{4}, \frac{7}{8}, \cdots $, then$a_7=?$5. Sequence is also called 6. Find the number of terms in an A.P. in which$a=3, d=7$, and$a_n=59$7. The sum of the series$-3+(-1)+(1) +3+5 +\cdots+ a_{16}$is 8. If$S_2, S_3, S_5$are the sums of$2n, 3n, 5n$terms of an A.P. then which one is true 9. If all the members of a sequence are real numbers then the sequence is called 10. If$\frac{1}{a}, \frac{1}{b}$and D\frac{1}{c}$ are in A.P. then which one is true:

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

12. The generl term $a_n$ of an A.P. is

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

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

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

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

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

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

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

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

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