# Number Series II – Number Series Questions on Arithmetic, Geometric and Harmonic Progressions

In this post, we will discuss Number Series Questions that are based on Arithmetic, Geometric and Harmonic Progressions for SSC Exams.
Number series Questions are the questions that need you to find the missing number in the series or to find the incorrect number placed in the series. These Number Series Questions always make their way in SSC CGL Exam. One must practice these questions in order to solve them within 30 seconds.In this post, we have discussed Number Series Questions that are frequently asked on Arithmetic, Geometric and Harmonic Progressions.
What is Arithmetic, Geometric and Harmonic Progression?

Arithmetic Progression

An arithmetic progression is a sequence of numbers in which a term is derived from the preceding term by adding or subtracting a fixed number, called the common difference "d."

For example 2, 4, 6, 8 is an arithmetic progression with a common difference 2 between them.

Geometric Progression

A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number, called the common ratio.

For example 4, -2, 1 is a geometric progression for which -1/2 is the common ratio.

Harmonic Progression

A series of terms is a harmonic progression series when their reciprocals are in arithmetic progression.

For example: 1/a, 1/a + d, 1/ a + 2d is a harmonic progression series because a, a + d, a + 2d are in in arithmetic progression.

Example of Number Series Questions on Arithmetic, Geometric and Harmonic Progressions

Question: 9, 16, 23, 30, 37, ?
Solution:
Step 1:
When we observe the series, we figure out that the numbers are increasing constantly.
The difference between two consecutive numbers is 7. When we add 7 to 9, we get 16 and when we add 7 to 16 we get 23. Likewise, when we keep on adding 7 to the successive numbers, we get the missing number as 44.

 9 16 23 30 37 ? 9 + 7 = 16 16 + 7 = 23 23 + 7 = 30 30 + 7 = 37 37 + 7 = 44 44

Therefore, 44 is the missing number.

Example of Number Series Questions on Arithmetic, Geometric and Harmonic Progressions

Question: 67, 58, 49, 41, 31, 22
Solution:
Step 1:
In this number series question, we need to find the incorrect number which is placed in the series.

When we observe the series we figure out that the series is decreasing constantly.
The difference between 67 and 58 is 9 and 58 and 49 is 9. So we can assume that the difference between two consecutive numbers is 9. Therefore to figure out the wrong number in the series we need to keep on subtracting 9 to check which number is incorrect.

 67 58 49 41 (40) 31 22 67 – 9 = 58 58 – 9 = 49 49 – 9 = 40 40 – 9 = 31 31 – 9 = 22 22

When we keep on subtracting 9 from two consecutive number we figure out that 49 – 9 = 40, but in the series 41 is placed. However, you need to verify the answer before jumping to the conclusion. So, we further subtract 49 – 9 = 40 and to verify we subtract 40 – 9 = 31 and 31 – 9 = 22.

Therefore, 41 is the incorrect number and it is suppose to be replaced with 40.

These type of questions often appear in SSC CGL Exam. As the SSC Exam is just 2 months away, start your preparation now!
Example of Number Series Questions on Arithmetic, Geometric and Harmonic Progression

Question:  14, 70, 350, ?, 8750, 43750
Solution:
Step 1:
When we observe the series, we figure out that the series is increasing at a very high rate. So, we can say that the number in series is being multiplied with a fixed number to give the succeeding number.

In this series, we find that each number is being multiplied with 5 to give the succeeding number.

 14 70 350 ? 8750 14 x 5 = 70 70 x 5 = 350 350 x 5 =1750 1750 x 5 = 8750 8750 x 5 = 43750

Therefore, The missing number is 1750

Example of Number Series Questions on Arithmetic, Geometric and Harmonic Progression

Question: 8000, 1600, 320, 64, ?
Solution:
Step 1:
In this number series question, we observe that the series is decreasing constantly. In this series, the number is being multiplied by a non-integer value i.e. 1/5 or 0.2.

 8000 1600 320 64 ? 8000 8000 x 0.2  = 1600 1600 x 0.2 = 320 320 x 0.2 = 64 64 x 0.2  = 12.8
Therefore, the missing number is 12.8.

Example of Number Series Questions on Arithmetic, Geometric and Harmonic Progression

Question: 1/3, 1/7, 1/11, ?, 1/19, 1/23
Solution:
Step 1:

This is a series with harmonic progression. To solve this number series question we need to take the reciprocal of the number to get arithmetic progression.

In the arithmetic series, we observe that the series is increasing gradually. When we find the difference between two terms, we get 4. Therefore the series is increasing by 4. So when we add 4 to 3 we get 7 and when we add 4 to 7 we get 11. Likewise, when we keep on adding 4 we get the missing number as 15.

 3 7 11 ? 19 3 + 4 = 7 7 + 4 = 11 11 + 4 = 15 15 + 4 = 19 19 + 4 = 23

Therefore, the missing number is 15.

Do write in the comment section, how this post helped you in solving number series questions.

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