Sequence and Series

Online MCQs Intermediate Mathematics chapter 6 of Sequence and Series with Question and Answers

Sequence and Series Quiz 4

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This post is about all the Online MCQs Sequence and Series Quiz from the First Year Mathematics Book (Part-I). Click the links below to start with the Online MCQs Sequence and Series Quiz.

Online Intermediate Mathematics Part 1 Chapter 6: Sequence and Series Quiz with Answers

1. The sum of $n$ A.Ms between $a$ and $b$ is equal to

 
 
 
 

2. If $\frac{a^{n+1} + b^{n+1}}{a^n + b^n}$ is A.M. between $a$ and $b$, then $n$ is equal to

 
 
 
 

3. Fifth term of $\frac{1}{3}, \frac{1}{5}, \frac{1}{7}, \cdots$ is

 
 
 
 

4. If $a$ and $b$ have opposite signs then the Geometric mean is

 
 
 
 

5. If $a_{n-1} = 2n+1$ then $a_n$ is equal to

 
 
 
 

6. If A, G, and H are Arithmetic, Geometric, and Harmonic means between two positive numbers, then

 
 
 
 

7. $\Sigma n$ is equal to

 
 
 
 

8. The general term of an H.P is

 
 
 
 

9. If A, G, and H are Arithmetic, Geometric, and Harmonic means between two negative numbers, then

 
 
 
 

10. $\Sigma n^3$ is equal to

 
 
 
 

11. If $a, ar^2, ar^4,\cdots$ form a G.P. then $\frac{1}{a}, \frac{1}{ar^2},  \frac{1}{ar^4}, \cdots$ is

 
 
 
 

12. H.M. between -2 and 8 equals

 
 
 
 

13. If $a$ and $b$ are two positive numbers, then

 
 
 
 

14. If $S_n=(n+1)^2$ then $S_{2n}$ is equal to

 
 
 
 

15. The GM between -2 and 8 is

 
 
 
 

16. $\Sigma n^2$ is equal to

 
 
 
 

17. The $n$th term of AP is

 
 
 
 

18. If $|r|<1$ then $S_n=$

 
 
 
 

19. Harmonic mean between two numbers $a$ and $b$ is

 
 
 
 

20. If $\frac{a^n + b^n}{a^{n-1} + b^{n-1}}$ is G.M. between $a$ and $b$, then $n$ is equal to

 
 
 
 

21. With the usual notation $n$th term of AP is

 
 
 
 

22. The harmonic mean between 2 and 8 is

 
 
 
 

23. $\frac{1}{2}, \frac{1}{7}, \frac{1}{12}, \cdots$ is

 
 
 
 

24. The general term of a sequence is $(-1)^n n^2$. Its 4th term is

 
 
 
 

25. If $G_1, G_2, \cdots, G_n$ are $n$ geometric means between $a$ and $b$ then $(G_1 G_2 \cdots G_n)^{\frac{1}{n}}$ is

 
 
 
 

26. The sum of 5 A.Ms between 2 & 8 is

 
 
 
 

27. The numbers $a-d$, $a$, $a+d$ are in

 
 
 
 

28. If both $x$ & $y$ are positive distinct real numbers, then the G.M. between $x$ and $y$ is

 
 
 
 

29. If $\frac{a^{n+1} + b^{n+1}}{a^n + b^n}$ is H.M. between $a$ and $b$, then $n$ is equal to

 
 
 
 

30. If $a$ and $b$ are two negative numbers, then

 
 
 
 

Intermediate Mathematics Sequence and Series Quiz with Answers

Online Intermediate Mathematics Sequence and Series Quiz

  • The general term of an H.P is
  • The harmonic mean between 2 and 8 is
  • If A, G, and H are Arithmetic, Geometric, and Harmonic means between two positive numbers, then
  • If A, G, and H are Arithmetic, Geometric, and Harmonic means between two negative numbers, then
  • If $a$ and $b$ are two negative numbers, then
  • If $a$ and $b$ are two positive numbers, then
  • If $a$ and $b$ have opposite signs then the Geometric mean is
  • If $\frac{a^{n+1} + b^{n+1}}{a^n + b^n}$ is A.M. between $a$ and $b$, then $n$ is equal to
  • If $\frac{a^n + b^n}{a^{n-1} + b^{n-1}}$ is G.M. between $a$ and $b$, then $n$ is equal to
  • If $\frac{a^{n+1} + b^{n+1}}{a^n + b^n}$ is H.M. between $a$ and $b$, then $n$ is equal to
  • If $a, ar^2, ar^4,\cdots$ form a G.P. then $\frac{1}{a}, \frac{1}{ar^2},  \frac{1}{ar^4}, \cdots$ is
  • $\Sigma n$ is equal to
  • $\Sigma n^2$ is equal to
  • $\Sigma n^3$ is equal to
  • If $S_n=(n+1)^2$ then $S_{2n}$ is equal to
  • The sum of $n$ A.Ms between $a$ and $b$ is equal to
  • The sum of 5 A.Ms between 2 & 8 is
  • If both $x$ & $y$ are positive distinct real numbers, then the G.M. between $x$ and $y$ is
  • The numbers $a-d$, $a$, $a+d$ are in
  • If $|r|<1$ then $S_n=$
  • If $a_{n-1} = 2n+1$ then $a_n$ is equal to
  • With the usual notation $n$th term of AP is
  • The GM between -2 and 8 is
  • H.M. between -2 and 8 equals
  • The $n$th term of AP is
  • Fifth term of $\frac{1}{3}, \frac{1}{5}, \frac{1}{7}, \cdots$ is
  • $\frac{1}{2}, \frac{1}{7}, \frac{1}{12}, \cdots$ is
  • If $G_1, G_2, \cdots, G_n$ are $n$ geometric means between $a$ and $b$ then $(G_1 G_2 \cdots G_n)^{\frac{1}{n}}$ is
  • Harmonic mean between two numbers $a$ and $b$ is
  • The general term of a sequence is $(-1)^n n^2$. Its 4th term is

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MCQs Sequence and Series Math 3

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This post is about an Online MCQs Sequence and Series Mathematics. A sequence is an ordered set of numbers formed according to some definite rule. Let us start with the MCQs Sequence and Series Mathematics Quiz.

MCQs Sequence and Series Mathematics
Please go to MCQs Sequence and Series Math 3 to view the test

MCQs Sequence and Series Math

  • The sum of the $n$ term of an arithmetic series $S_n$ is equal to
  • The sum of the $n$ term of an arithmetic series in $S_n$ is equal to
  • For any G.P. the common ratio $r$ is equal to
  • No term of a G.P. is
  • The general term of a G.P. is
  • If $a, G, b$ are in G.P. then
  • If $a, G, b$ are in G.P., then $G$ is called
  • If $G_1, G_2, \cdots, G_n$ be geometric means between $a$ and $b$, then $G=$
  • The sum of the $n$ term of a geometric series $S_n$ is equal to
  • The sum of infinite geometric series is valid if
  • For the series $1+5+25+125+\cdots +\cdots \infty$, the sum is
  • An infinite geometric series is convergent if
  • An infinite geometric series is divergent if
  • If the sum of a series is defined, then it is called
  • If the sum of a series is not defined, then it is called
  • If the series $\frac{x}{2} + \frac{x^2}{4} + \frac{x^3}{8}+\cdots$ is convergent then
  • If the series $\frac{2}{3}x+ \frac{4}{9}x^2+\frac{8}{27}x^3\cdots $ is divergent, then
  • The interval in which series $1+2x+4x^2+8x^3+\cdots$ is convergent is
  • If the reciprocals of the terms of a sequence form an A.P., then it is
  • The $n$th term of $\frac{1}{2}, \frac{1}{5}, \frac{1}{8}, \cdots$ is

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Sequence and Series Quizzes

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This post is about all the Online MCQs Sequence and Series Quizzes from the Mathematics Book of Part I (First Year). Click the links below to start with Online MCQs Sequence and Series Quizzes.

Sequence and Series Quizzes with Answers

MCQs Sequence and Series Quiz 4MCQs Sequence and Series Math 3
MCQs Sequence and Series 2MCQs Sequence and Series 1

Series and Series

A sequence is an ordered set of numbers formed according to some definite rule. 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 $n\in N$.

MCQs Sequence and Series Quizzes Mathematics Class 11

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, 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.

Progression

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

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