All questions of Series Completion and Inserting for Class 8 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).

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 provided is: 3, 8, 15, 24, 35, 48. To find the next number, we need to identify the pattern that governs the sequence.
Finding the Differences
First, we can look at the differences between consecutive numbers:

• 8 - 3 = 5
• 15 - 8 = 7
• 24 - 15 = 9
• 35 - 24 = 11
• 48 - 35 = 13

The differences are: 5, 7, 9, 11, 13.
Analyzing the Differences
Notice that the differences themselves form a sequence:

• 5, 7, 9, 11, 13

These numbers increase by 2 each time. This indicates that the next difference will be:

• 13 + 2 = 15

Calculating the Next Term
To find the next term in our original sequence, we add this next difference (15) to the last number (48):

• 48 + 15 = 63

Thus, the next number in the sequence is 63.
Conclusion
Therefore, the correct answer is option 'C' which is 63.

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).