All questions of Series Completion and Inserting for Class 6 Exam

Missing Number in Series

Given Series: 13, 24, 46, 90, 178, ?

Pattern in the Series:
- The difference between consecutive numbers in the series is increasing.
- 24 - 13 = 11
- 46 - 24 = 22
- 90 - 46 = 44
- 178 - 90 = 88

Identifying the Missing Number:
To find the missing number, we need to continue the pattern of increasing differences between consecutive numbers.
- The next difference should be 88 * 2 = 176.
- So, the missing number can be calculated as: 178 + 176 = 354.
Therefore, the missing number in the series is 354 (option c).

The given series is 4, 18, ___, 100, 180, 294, 448. We need to find the missing number in the series.

To solve this problem, we need to identify the pattern or relationship between the numbers in the series.

Pattern Analysis:
Let's analyze the given series to identify any pattern or relationship between the numbers.

- The first number in the series is 4.
- The second number is obtained by multiplying the first number by 4 and then adding 2. So, 4 * 4 + 2 = 18.
- The third number can be obtained by multiplying the second number by 4 and then subtracting 6. So, 18 * 4 - 6 = 66.
- The fourth number is obtained by multiplying the third number by 4 and then adding 2. So, 66 * 4 + 2 = 266.
- The fifth number is obtained by multiplying the fourth number by 4 and then subtracting 20. So, 266 * 4 - 20 = 100.
- The sixth number is obtained by multiplying the fifth number by 4 and then adding 2. So, 100 * 4 + 2 = 402.
- The seventh number is obtained by multiplying the sixth number by 4 and then subtracting 6. So, 402 * 4 - 6 = 1594.

We can see that there is an alternating pattern of multiplying by 4 and subtracting or adding a constant value in each step. Using this pattern, we can find the missing number.

Calculating the Missing Number:
To find the missing number, we need to apply the pattern to the previous number in the series.

- The sixth number is 402, which was obtained by multiplying the fifth number (100) by 4 and then adding 2.
- So, to find the missing number, we need to apply the pattern to the sixth number.

Applying the pattern:
The sixth number (402) was obtained by multiplying the fifth number (100) by 4 and then adding 2. So, the missing number can be obtained by multiplying 402 by 4 and then subtracting 6.

Missing number = 402 * 4 - 6
= 1608 - 6
= 1602

Therefore, the missing number in the given series is 1602.

Hence, the correct answer is option C) 1602.

Explanation:
The given series is 25: 37:: 49: ?

To find the missing number, we need to observe the pattern in the given series.

Pattern:
If we look at the given series, we can see that each pair of numbers has a difference of 12.

Let's break down the series into pairs:

- 25 and 37: The difference is 37 - 25 = 12
- 49 and ?: We need to find the missing number.

Calculation:
To find the missing number, we can add 12 to the second number in the pair.

- 49 + 12 = 61

Therefore, the missing number is 61.

Verification:
We can verify our answer by checking if the pattern holds true for the rest of the series:

- 37 and 49: The difference is 49 - 37 = 12
- 49 and 61: The difference is 61 - 49 = 12

Since the pattern holds true for the entire series, we can confidently say that the missing number is 61.

Conclusion:
The missing number in the series 25: 37:: 49: ? is 61. Therefore, option C (65) is incorrect. The correct answer is option C (61).

The given sequence is 9, 25, 49, 81, 121, ?.

Sequence Analysis:
To find the pattern in the given sequence, we need to look for the relationship between the numbers. Let's analyze the sequence step by step.

Step 1:
The given sequence is a list of perfect squares. Each number in the sequence is the square of a specific natural number.

9 = 3^2
25 = 5^2
49 = 7^2
81 = 9^2
121 = 11^2

Step 2:
The pattern in the given sequence is that each number is the square of the next odd number. For example, 9 is the square of 3, 25 is the square of 5, and so on.

Step 3:
To find the next number in the sequence, we need to find the square of the next odd number after 11.

The next odd number after 11 is 13. So, the next number in the sequence is 13^2 = 169.

Conclusion:
Therefore, the missing number in the sequence is 169.

Answer:
The correct answer is option 'D' (169).

Understanding the Sequence
The sequence given is: 27, 56, 114, 230, 462, 926. To find the next number, we first need to identify a pattern in the differences between consecutive terms.
Identifying Differences
- 56 - 27 = 29
- 114 - 56 = 58
- 230 - 114 = 116
- 462 - 230 = 232
- 926 - 462 = 464
The differences between the terms are: 29, 58, 116, 232, 464.
Observing the Pattern in Differences
Now, let's analyze the differences:
- 29 (which is 29)
- 58 (which is 2 * 29)
- 116 (which is 4 * 29)
- 232 (which is 8 * 29)
- 464 (which is 16 * 29)
We can see that each difference is double the previous difference.
Calculating the Next Difference
Following this pattern, the next difference should be:
- 464 * 2 = 928
Finding the Next Term
To find the next term in the sequence, add the last term (926) to the next difference (928):
- 926 + 928 = 1854
Conclusion
Therefore, the next number in the sequence is 1854, making option 'B' the correct answer.

Given Series: 2, 3, 12, 37, 86, 166, 288

To find out the wrong term in the given series, let's analyze the pattern of the series.

Pattern Analysis:
- The series does not follow a simple arithmetic or geometric progression.
- On observing the differences between consecutive terms, we can see that the differences are not constant.
- Let's calculate the differences:
- Difference between the 2nd and 1st terms: 3 - 2 = 1
- Difference between the 3rd and 2nd terms: 12 - 3 = 9
- Difference between the 4th and 3rd terms: 37 - 12 = 25
- Difference between the 5th and 4th terms: 86 - 37 = 49
- Difference between the 6th and 5th terms: 166 - 86 = 80
- Difference between the 7th and 6th terms: 288 - 166 = 122

Pattern:
The differences are not following a clear pattern. However, if we observe the differences themselves, we can see that they are increasing by multiples of 8: 1, 9, 25, 49, 80, 122.

Finding the Wrong Term:
To find the wrong term, we need to search for a term that does not fit the pattern. Let's calculate the differences between the actual terms and the expected terms based on the pattern.

- Expected difference between the 2nd and 1st terms: 2 + 8 = 10
- Expected difference between the 3rd and 2nd terms: 3 + 8 = 11
- Expected difference between the 4th and 3rd terms: 12 + 8 = 20
- Expected difference between the 5th and 4th terms: 37 + 8 = 45
- Expected difference between the 6th and 5th terms: 86 + 8 = 94
- Expected difference between the 7th and 6th terms: 166 + 8 = 174

Comparing the expected differences with the actual differences, we can see that the difference between the 6th and 5th terms (80) does not match the expected difference (94).

Therefore, the wrong term in the given series is 166 (option D).