AP GP HP Questions and Answers

September 19, 2023

AP, GP and HP Questions and Answers

In this Page AP and GP and HP Questions is given for Practices. This will help in you Solving Different Questions in Different Examinations.
Questions of AP and GP and HP

General form of AP ,GP and HP

Arithmetic Progression (AP):

The general form of an AP is : a, a + d, a + 2d, a + 3d, …, where a is the first term and d is the common difference

Geometric Progression (GP):

The general form of an GP is : a, ar, ar^2, ar^3, …, where a is the first term and r is the common ratio.

Harmonic Progression (HP):

The general form of an HP is : 1/a, 1/(a + d), 1/(a + 2d), 1/(a + 3d), …, where a is the first term and d is the common difference.

Examples

Example of Arithmetic Progression  4 , 8 ,12 , 16…

Example of Geometric Progression  2 , 4, 8 , 16 , 32..

Example of Harmonic Progression  \frac{1}{2} , \frac{1}{4} , \frac{1}{6}…

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Question 1

Time: 00:00:00
The 9th term of a GP is 16 times more than its 5th term. If its 7th term is 96, then find the first term.

3.9

3.9

1.5

1.5

9.2

9.2

7.02

7.02

Question 2

Time: 00:00:00
X and Y are 2 numbers whose Arithmetic mean is 61 and Geometric Mean is 11. If X > Y What will be X’s value then?

120

120

121

121

125

125

128

128

Question 3

Time: 00:00:00
If a sequence is given as 1,3,5,7,9, and so on, then what will be the sum of first 50 term?

2000

2000

2500

2500

3000

3000

3500

3500

Question 4

Time: 00:00:00
What will be the sum, if the series is: 1 + 2·5 + 4 + 5·5 + . . . + 100.

2345.6

2345.6

2545.2

2545.2

3383.5

3383.5

4155.5

4155.5

Question 5

Time: 00:00:00
4 is the first term in an AP and the total of first 9 terms is twice the total of the initial 6 terms. What will be the common difference?

1.96

1.96

7.21

7.21

2.25

2.25

2

2

Question 6

Time: 00:00:00
If the AP is 6 , 9.5 , 13 . . ., then what will be the sum of first 22 terms

679

679

876

876

940.5

940.5

999.5

999.5

Question 7

Time: 00:00:00
If the sum of c terms sum in AP and e terms are equal, then find the sum of first (c+e) terms?

Zero

Zero

1

1

infinite

infinite

-1

-1

Question 8

Time: 00:00:00
In an arithmetic series if two numbers sum is 9, and total of their cubes is 243, then find out the total of their squares?

35

35

40

40

41

41

45

45

Question 9

Time: 00:00:00
If initial 48 terms sum is equivalent to four times of the initial 36 terms. Find out the total of the first 30 terms?

Zero

Zero

30

30

45

45

5

5

Question 10

Time: 00:00:00
In an arithmetic series if two numbers sum is 12, and total of their cubes is 576, then find out the total of their squares?

35

35

40

40

41

41

80

80

Question 11

Time: 00:00:00
If p, q, r pre in h.p, then q is connected with p and r as

2\frac{1}{q} = \frac{1}{p}+\frac{1}{r}

2\frac{1}{q} = \frac{1}{p}+\frac{1}{r}

2\frac{1}{r} = \frac{1}{q}+\frac{1}{p}

2\frac{1}{r} = \frac{1}{q}+\frac{1}{p}

2\frac{1}{q} = \frac{1}{p}-\frac{1}{r}

2\frac{1}{q} = \frac{1}{p}-\frac{1}{r}

None of the mentioned

None of the mentioned

Question 12

Time: 00:00:00
For 2 number P and Q, Harmonic Mean among them will be?

\frac{2q}{(p+q)}

\frac{2q}{(p+q)}

\frac{2pq}{(p+q)}

\frac{2pq}{(p+q)}

\frac{(p+q)}{2pq}

\frac{(p+q)}{2pq}

None

None

Question 13

Time: 00:00:00
Find the 6th term of the series in which t_{1}=7 and t_{n}= −3t_{n-1} ?

567

567

875

875

-1701

-1701

1800

1800

Question 14

Time: 00:00:00
G.M of A is 20, G.M of B is 25. Find out the G.M of ab is?

20.50

20.50

21.62

21.62

22

22

22.56

22.56

Question 15

Time: 00:00:00
If a_{1} is First term and a_{9} is ninth term. Find out the common ratio, r, for the Geometric sequence?

r = (\frac{a_{9}}{a_{8}})^{\frac{1}{8}}

r = (\frac{a_{9}}{a_{8}})^{\frac{1}{8}}

r = (\frac{a_{9}}{a_{8}})^{\frac{1}{7}}

r = (\frac{a_{9}}{a_{8}})^{\frac{1}{7}}

r = (\frac{a_{9}}{a_{8}})^{\frac{1}{10}}

r = (\frac{a_{9}}{a_{8}})^{\frac{1}{10}}

r = (\frac{a_{9}}{a_{8}})^{\frac{1}{14}}

r = (\frac{a_{9}}{a_{8}})^{\frac{1}{14}}

Question 16

Time: 00:00:00
If the geometric series is 4, 12, 36,..., then find the 9th term.

6561

6561

26244

26244

19683

19683

20096

20096

Question 17

Time: 00:00:00
If for two different digits, G.M.=22 and A.M.=26, find their H.M?

15

15

16.43

16.43

17.54

17.54

18.61

18.61

Question 18

Time: 00:00:00
If the Arithmetic Mean between two digits is 1, then Harmonic Mean is the square of their Geometric Mean.

True

True

False

False

Partial a and b

Partial a and b

Cannot be determined

Cannot be determined

Question 19

Time: 00:00:00
If arithmetic mean of  two numbers  is 28 and their geometric mean is 15, then what will be the sum of numbers?

30

30

40

40

52

52

56

56

Question 20

Time: 00:00:00
Find the harmonic mean of two numbers 15 and 31?

15.31

15.31

17.43

17.43

20.21

20.21

24.21

24.21

Question 21

Time: 00:00:00
If there are two sets with 100 and 69 as harmonic mean and comprising 25 and 23 observations then the combined harmonic mean....?

76.34

76.34

82.28

82.28

90

90

101.12

101.12

Question 22

Time: 00:00:00
If arithmetic mean is 30 and geometric mean 26 of two values, then find out the harmonic mean?

22.53

22.53

23.56

23.56

24.76

24.76

24.56

24.56

Question 23

Time: 00:00:00
The harmonic mean of 15,12,18,20 will be ?

13.45

13.45

14.23

14.23

16.66

16.66

18.98

18.98

Question 24

Time: 00:00:00
Below given is the age and total number of students of final year in college Xavier’s. Find out the harmonic means of this?





















Age(years) 17 18 19 20 21
Number of Scholars 12 15 23 17 13

17

17

18.56

18.56

19.04

19.04

20

20

Question 25

Time: 00:00:00
Find the harmonic mean of 2 numbers whose G.M. and A.M. is 15 and 18?

10

10

11.5

11.5

12.5

12.5

13

13

Question 26

Time: 00:00:00
Find harmonic mean, if A.M is 40 and G.M is 36?

29.4

29.4

30

30

32.4

32.4

33

33

Question 27

Time: 00:00:00
Find the harmonic mean of the following data {5, 9, 7, 10, 8, 5}?

6.66

6.66

7

7

6.89

6.89

8

8

Question 28

Time: 00:00:00
Find Arithmetic Mean and Harmonic Mean from the following averages:
26.4, 29.8 and 25.8

27.3, 27.77

27.3, 27.77

28.70, 28.43

28.70, 28.43

35.65, 33.34

35.65, 33.34

31.21, 42.12

31.21, 42.12

Question 29

Time: 00:00:00
The 9th term of \frac{1}{4} ,\frac{1}{8},\frac{1}{12},\frac{1}{16} ……… will be?

\frac{1}{35}

\frac{1}{35}

\frac{1}{36}

\frac{1}{36}

\frac{1}{39}

\frac{1}{39}

None of the mentioned

None of the mentioned

Question 30

Time: 00:00:00
If P, Q, R are in hp then P-1, Q-1, R-1 are in

GP

GP

HP

HP

AP

AP

None of the above

None of the above

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