All questions of Series Completion and Inserting for Class 6 Exam

The pattern here is that each number is the product of the previous two numbers, plus the sum of the previous two numbers.

For example:

- 3 = 1*2 + 1+2
- 4 = 2*1 + 2+3
- 10 = 3*2 + 3+4
- 33 = 4*3 + 4+10
- 136 = 10*4 + 10+33

So to find the next number in the sequence, we need to apply the same formula:

- ? = 33*10 + 33+136
- ? = 330+169

Therefore, the next number in the sequence is 499.

None of the given options match this answer, so the correct answer is not listed.

The correct answer is option c because:-

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.

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).

Understanding the Series
The given series is: 1, 2, 10, 37, 101, __.
To identify the pattern, let's look at the differences between the consecutive terms.
Calculating Differences
- 2 - 1 = 1
- 10 - 2 = 8
- 37 - 10 = 27
- 101 - 37 = 64
This gives us a new series of differences: 1, 8, 27, 64.
Identifying a Pattern in Differences
Now, let's analyze these differences:
- 1 = 1³
- 8 = 2³
- 27 = 3³
- 64 = 4³
The differences are the cubes of consecutive integers: \( n^3 \), where \( n \) is the position in the series.
Finding the Next Difference
Following this pattern, the next difference would be:
- 5³ = 125
Calculating the Next Term
Now, we can find the next term in the original series:
- Previous term: 101
- Next difference: 125
So,
101 + 125 = 226.
Conclusion
Thus, the next term in the series is 226.
Correct answer: option 'D'.

Pattern Analysis:
The given sequence of numbers is: 16, 22, 30, 40, 52, 66, 82, ?

Identifying the Pattern:
- The difference between consecutive numbers is as follows:
- 22 - 16 = 6
- 30 - 22 = 8
- 40 - 30 = 10
- 52 - 40 = 12
- 66 - 52 = 14
- 82 - 66 = 16

Applying the Pattern:
Following the pattern of increasing differences between consecutive numbers, the next difference should be 18.

Finding the Missing Number:
- Adding 18 to the last number in the sequence (82), we get:
- 82 + 18 = 100
Therefore, the missing number in the sequence is 100.

Final Answer:
The missing number in the sequence 16, 22, 30, 40, 52, 66, 82, ? is 100 (Option A).

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.

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.