Mathematics Part1

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

 $G^2=AH$

 A>G>H

 All of these

 A, G, H, are in G.P

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

 $n[a+(n-1)d]$

 $a+(n-1)d$

 $n\left(\frac{a+b}{2}\right)$

 $n(a+b)$

3. $\Sigma n$ is equal to

 $\frac{n(n+1)(2n+1)}{6}$

 $n^2$

 $\frac{n^2(n+1)^2}{2}$

 $\frac{n(n+1)}{2}$

4. The general term of an H.P is

 $a_n=a+(n-1)d$

 $a_n = \frac{1}{a+(n+1)d}$

 $a_n = \frac{1}{a+nd}$

 $a_n = \frac{1}{a+(n-1)d}$

5. The GM between -2 and 8 is

 16 or -16

 4 or -4

 4i or -4i

 3 or -5

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

 1

 0

 1/2

 -1

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

 $\frac{-16}{3}$

 $\frac{-16}{5}$

 $\frac{-5}{16}$

 $\frac{-3}{16}$

8. The $n$th term of AP is

 $\frac{a_1}{n}+d$

 $a_1 + (n-1)d$

 $a_n+nd$

 $na_1+d$

9. 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

 a reciprocal sequence

 an A.P.

 an H.P.

 a G.P.

10. 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

 $\frac{2ab}{a+b}$

 $\frac{a+b}{2}$

 $\frac{a+b}{2ab}$

 $\sqrt{ab}$

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

 Harmonic series

 GP

 An AP

 HP

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

 $\frac{a_1(1-r^n)}{1-r}$

 $\frac{a_1(r^n-1)}{r-1}$

 $\frac{a_1(r^n-1)}{1-r}$

 $\frac{a_1(1-r^n)}{r-1}$

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

 $G^2=AH$

 A < G < H

 A, G, H are in G.P.

 All of these

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

 50

 10

 25

 40

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

 arithmetic progression

 harmonic progression

 geometric progression

 harmonic series

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

 A > G > H

 A < G < H

 A = G = H

 A $\le$ G $\le$ H

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

 -4

 16

 -16

 4

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

 $\frac{n^2(n+1)^2}{4}$

 $\frac{n(n+1)(2n+1)}{6}$

 $\frac{n(n+!)}{2}$

 $\frac{n(n+1)^2}{2}$

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

 1/2

 -1

 1

 0

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

 $a_n = a_1 + a_{n+1}$

 $a_n=a_1+(n+1)d$

 $a_n = a_1 + (n-1)d$

 $a_n=a_1 – (n-1)d$

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

 Non zero real number

 Negative

 Real number

 An imaginary number

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

 $\frac{a+b}{2ab}$

 $\frac{2ab}{a+b}$

 $\frac{a+b}{2}$

 $\pm\sqrt{ab}$

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

 1/2

 0

 -1

 1

24. The harmonic mean between 2 and 8 is

 5

 16/5

 5/16

 $\pm$ 4

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

 $4n^2+4n+1$

 $(2n-1)^2$

 $2n+1$

 cannot be determined

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

 none of these

 greater than A.M.

 equal to A.M.

 less than their A.M.

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

 $2n+1$

 $2n+3$

 $2n-1$

 $2n-3$

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

 A < G< H

 A > G > H

 A = G = H

 A $\ge$ G $\ge$ H

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

 1/11

 9

 1/9

 11

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

 $\frac{n(n+1)(2n+1)}{6}$

 $n^2$

 $\frac{n(n+1)}{2}$

 $\frac{n^2(n+1)^2}{2}$

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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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