# MCQS Sequence and Series 1

This post is about Online MCQs of sequence and series:

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

MCQs Mathematics covers the topic of the Number system for the preparation of Intermediate mathematics.

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

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

3. The sum of terms of a sequence is called

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

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

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

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

8. A sequence is also known as

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

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

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

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

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

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

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

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

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

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

19. The last term of an infinite sequence

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

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

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