Mathematics Part1

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.

Online Sequence and Series First Year Mathematics Quiz With Answers

1. If the series $\frac{x}{2} + \frac{x^2}{4} + \frac{x^3}{8}+\cdots$ is convergent then

 $0<x<2$

 $|x|\ge 2$

 $|x| \le 1$

 $|x| \le 2$

2. No term of a G.P. is

 Imaginary number

 1

 0

 Negative

3. If the sum of a series is defined, then it is called

 Geometric series

 Finite series

 Divergent series

 Convergent series

4. If the reciprocals of the terms of a sequence form an A.P., then it is

 Harmonic sequence

 Series

 Reciprocal sequence

 Arithmetic sequence

5. The Sum of the $n$ term of an arithmetic series $S_n$ is equal to

 $\frac{n}{2}[2a+(n-1)d]$

 $\frac{n}{2}[2a+(n+1)d]$

 $\frac{n}{2}[2a+l]$

 $\frac{n}{2}[a+(n-1)d]$

6. An infinite geometric series is convergent if

 $|r|>1$

 $|r|=1$

 $|r|\ge1$

 $|r|<1$

7. For any G.P. the common ratio $r$ is equal to

 $\frac{a_n-1}{a_n}$

 $\frac{a_n}{a_n-1}$

 $a_{n+1}-a_n$ for $n\in N, n>1$

 $\frac{a_n}{a_n+1}$

8. The interval in which series $1+2x+4x^2+8x^3+\cdots$ is convergent is

 $-\frac{1}{2}<x<\frac{1}{2}$

 $-2<x<2$

 $|x|<1$

 $|2x|>1$

9. The general term of a G.P. is

 $a_n=ar^{n-1}$

 $a_n=\frac{a}{r^n-1}$

 $a_n=ar^{n+1}$

 $a_n=ar^n$

10. If the sum of a series is not defined, then it is called

 Divergent series

 Infinite series

 Finite series

 Convergent series

11. An infinite geometric series is divergent if

 $|r|<1$

 $|r|>1$

 $|r|\ne 1$

 $r=0$

12. The sum of infinite geometric series is valid if

 $|r|>1$

 $|r|=1$

 $|r|<1$

 $|r| \ge 1$

13. The $n$th term of $\frac{1}{2}, \frac{1}{5}, \frac{1}{8}, \cdots$ is

 $2n+1$

 $3n-1$

 $\frac{1}{3n-1}$

 $\frac{1}{3n+1}$

14. If the series $\frac{2}{3}x+ \frac{4}{9}x^2+\frac{8}{27}x^3\cdots $ is divergent, then

 $\frac{2}{3}\big|x\big|<1$

 $\big|\frac{2}{3}x\big|<1$

 $\big|\frac{2}{3}x\big| \ge 1$

 $|x|\ge1$

15. The sum of the $n$ term of a geometric series $S_n$ is equal to

 $ar^{n-1}$, for $r \ne 1$

 $\frac{a(1-r^{n-1})}{r-1}$

 $\frac{a(1-r^n)}{1 – r}$

 $\frac{a(r^n-1)}{1-r}$

16. For the series $1+5+25+125+\cdots +\cdots \infty$, the sum is

 $4$

 Not defined

 $\frac{1-5^n}{-4}$

 $-4$

17. The sum of the $n$ term of an arithmetic series in $S_n$ is equal to

 $\frac{a+a_n}{2}$

 $\frac{n}{n}(a_1-1)$

 $n(a_1+a_n)$

 $\frac{n}{n}(a_1+a_n)$

18. If $G_1, G_2, \cdots, G_n$ be geometric means between $a$ and $b$, then $G=$

 $\frac{1}{n}(G_1, G_2, \cdots, G_n)$

 $\frac{G_1+G_2+\cdots + G_n}{n}$

 $(G_1G_2\cdots G_n)^{\frac{1}{n}}$

 $\sqrt{G_1G_2\cdots G_n}$

19. If $a, G, b$ are in G.P. then

 $G=\frac{a+b}{2}$

 $G=\pm \sqrt{ab}$

 $G=ab$

 $G=\frac{2ab}{a+b}$

20. If $a, G, b$ are in G.P., then $G$ is called

 Geometric mean

 Common ratio

 Centre

 Geometric series

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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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