# AP GP HP Questions and Answers

## AP and 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.

### Definition of AP and GP and HP

Arithmetic Progression:

An Arithmetic progression is a categorization of numbers in which each number is obtained from its preceding number either by adding or by subtracting a constant number known as the common difference “d”.

Geometric Progression:

A Geometric Progression is an arrangement where each number is obtained by either multiplying or dividing the previous number with a specific number called the common ratio “r”.

Harmonic Progression:

Any series is known to be a Harmonic Progression series when its correlatives are in Arithmetic progression.

### Examples

Example of Harmonic 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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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