The number series questions and answers are provided here to help students understand the concept quickly. One of the most important topics which is very useful in school and competitive examinations is the number series. The questions provided here can be used by students to get a fast overview of the topics, and to practise them so that they are more familiar with the concept. Practise the question and cross-verify your answers with the solutions provided on this page. To know more about sequence and series, click here.
| Series Definition: In Maths, the series is defined as the sum of all elements of a sequence. The order of elements is not important in series. The series can be classified into finite series and infinite series.
Finite series: The series has a finite number of elements (Example: 1 + 2 + 3 + 4 + 5). Infinite series : The series has an infinite number of elements (Example: 1 + 2 + 3 + 4 + 5 + …) Number Series Definition: The number series is defined as the sequence or series of numbers that follow a specific pattern. |
Go through the below-given number series questions and answers and practise them as well.
Series Questions with Solutions
1. Write the arithmetic series for the given sequence 5, 10, 15, 20, 25, ….., xn.
Solution:
Given sequence: 5, 10, 15, 20, 25, ……, xn.
Therefore, the arithmetic series for the given sequence is 5 + 10 + 15 + 20 + 25 + …… + xn.
2. Write the formula for arithmetic and geometric series.
Solution:
As we know, the arithmetic sequence is of the form: a, a + d, a + 2d, a + 3d, …
Hence, the formula for arithmetic series is a + (a + d) + (a + 2d) + (a + 3d) + …
Similarly, the geometric sequence is of the form: a, ar, ar2,…., ar(n-1),…
Hence, the formula for geometric series is a + ar + ar2 + …+ ar(n-1)+ …
3. Find the missing number in the given series 13, 24, 46, 90, 178, ?.
Solution:
Given series: 13, 24, 46, 90, 178, ?.
24 – 13 = 11
46 – 24 = 22
90 – 46 = 44
178 – 90 = 88
The logic used here is that the difference between two successive numbers is doubled consecutively.
So, if 88 is doubled, we get 176.
Hence, 178 + 176 = 354.
Thus, the missing term in the sequence is 354.
Therefore, the complete series is 13, 24, 46, 90, 178, 354.
4. Find the missing number in the given series 4, 18, ___, 100, 180, 294, 448.
Solution:
The given sequence is obtained as follows:
23 – 22 = 8 – 4 = 4
33 – 32 = 27 – 9 = 18
43 – 42 = 64 – 16 = 48
53 – 52 = 125 – 25 = 100
63 – 62 = 216 – 36 = 180
73 – 72 = 343 – 49 = 294
83 – 82 = 512 – 64 = 448
Hence, the missing number in the series is 48.
Therefore, the complete series is 4, 18, 48, 100, 180, 294, 448.
5. Determine the missing numbers in the series 5, 6, 9, 14, 21, ?.
Solution:
Given the number series: 5, 6, 9, 14, 21, ?.
5 + 1 = 6
6 + 3 = 9
9 + 5 = 14
14 + 7 = 21
21 + 9 = 30.
Hence, the missing number here is 30.
Here, the series follows a pattern of the sum of consecutive odd numbers.
So, the complete number series is 5, 6, 9, 14, 21, 30.
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6. Complete the series 1, 2, 10, 37, 101, __.
Solution:
Given series: 1, 2, 10, 37, 101, ___.
1 + 13 = 1 + 1 = 2
2 + 23 = 2 + 8 = 10
10 + 33 = 10 + 27 = 37
37 + 43 = 37 + 64 = 101
101 + 53 = 101+ 125 = 226
Thus, the given series follows a pattern of the sum of cubes of the consecutive natural numbers.
So, the complete series 1, 2, 10, 37, 101, 226.
7. Find out the wrong term in the given series: 2, 3, 12, 37, 86, 166, 288.
Solution:
Given series: 2, 3, 12, 37, 86, 166, 288.
2 + 12 = 2 + 1 = 3
3 + 32 = 3 + 9 = 12
12 + 52 = 12 + 25 = 37
37 + 72 = 37 + 49 = 86
86 + 92 = 86 + 81 = 167
167 + 112 = 167 + 121 = 288.
Here, the series follows a pattern of addition of the square of the consecutive odd numbers.
So, from the given number series 2, 3, 12, 37, 86, 166, 288, the wrong term is 166, because it should be 167.
8. Find the missing number 25: 37:: 49:?
Solution:
Here, 52 = 25 and (5+1)2 + 1 = 37
Similarly, 72 = 49 and (7+1)2 + 1 = 65.
Hence, the missing number is 65.
9. 11 : 121 :: 13 : ____. Find the missing value.
Solution:
Here, 112 = 121
So, 132= 169
So, the missing number is 169.
I.e., 11: 121 :: 13 : 169.
10. Find out the missing term in the given series: 11, 17, 39, 85, ?.
Solution:
Given series: 11, 17, 39, 85, ?.
11 + (32 – 3) = 11 + 6 = 17
17 + (52 – 3) = 17 + 22 = 39
39 + (72 – 3) = 39 + 46 = 85
85 + (92 – 3) = 85 + 78 = 163
Therefore, the missing number in the given series is 163.
I.e., 11, 17, 39, 85, 163.
Practice Questions
- Write the series for the given sequence 1, 3, 5, 7, 9, ….
- Find the missing number in the series 3, 5, 5, 19, 7, 41, 9, ?.
- Determine the missing number in the series 13, 15, 21, 33, 53, ___.
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