All questions of Series for SSC CGL Exam

Understanding the Series
To solve the series 5, 7, 11, 17, 25, ?, we need to identify the pattern in the sequence.
Identifying Differences
Let's look at the differences between consecutive terms:
- 7 - 5 = 2
- 11 - 7 = 4
- 17 - 11 = 6
- 25 - 17 = 8
The differences are: 2, 4, 6, 8.
Recognizing the Pattern
We can observe that the differences themselves form an increasing sequence:
- The first difference is 2 (2 = 2)
- The second difference is 4 (4 = 2 + 2)
- The third difference is 6 (6 = 4 + 2)
- The fourth difference is 8 (8 = 6 + 2)
This indicates that each difference increases by 2.
Calculating the Next Difference
Following this pattern, the next difference should be:
- Next difference = 8 + 2 = 10
Finding the Missing Term
Now, we add this next difference to the last term in the series:
- 25 + 10 = 35
Thus, the missing term is 35.
Conclusion
The correct answer to the series 5, 7, 11, 17, 25, ? is:
- a) 35
This confirms that option 'A' is indeed correct.

Series Explanation:
The given series is a combination of two different patterns. Let's break down the series into two separate patterns to understand it better.

Pattern 1:
1, 5, 11, 17, ...

In the first pattern, the numbers are increasing by 4. So, we can find the next number by adding 4 to the previous number.

1 + 4 = 5
5 + 4 = 9
11 + 4 = 15
17 + 4 = 21

Pattern 2:
0, 12, 24, 36, ...

In the second pattern, the numbers are increasing by 12. So, we can find the next number by adding 12 to the previous number.

0 + 12 = 12
12 + 12 = 24
24 + 12 = 36
36 + 12 = 48

Combining the Patterns:
Now, let's combine both patterns to find the missing number.

1, 0, 5, 12, 11, 17, 24, 1330, 36, ...

From the pattern 1, we can see that the missing number should be 9 because it follows the pattern of increasing by 4.

1, 0, 5, 12, 11, 17, 24, 1330, 36, 9

From the pattern 2, we can see that the missing number should be 48 because it follows the pattern of increasing by 12.

1, 0, 5, 12, 11, 17, 24, 1330, 36, 9, 48

Therefore, the correct number to fill in the blank and complete the series is 48.

Final Answer:
The correct option that will fill in the blank and complete the series is option C) 48.

Series Pattern:
The given series is: L, K, I, F, B, W, __________.

Observations:
- The series consists of alphabetical letters.
- The letters in the series are not in alphabetical order.
- The letters are not following any specific pattern based on their positions in the English alphabet.

Analysis:
- As the series does not follow any pattern based on the positions of the letters in the English alphabet, we need to look for alternative patterns or relationships between the letters.

Pattern 1:
- If we consider the positions of the letters in the English alphabet, we can observe that the positions of the letters in the given series are decreasing by 1.
- Starting from L (position 12), each subsequent letter has a position that is 1 less than the previous letter.

Pattern 2:
- If we consider the positions of the letters in the English alphabet and convert them to corresponding numbers (A = 1, B = 2, C = 3, ...), we can observe that the difference between the numbers of the letters in the given series is decreasing by 1.
- Starting from L (position 12, number 12), each subsequent letter has a number that is 3 less than the previous letter.

Pattern 3:
- If we consider the positions of the letters in the English alphabet and convert them to corresponding numbers (A = 1, B = 2, C = 3, ...), we can also observe that the numbers of the letters in the given series are alternating between odd and even.
- L (position 12, number 12) and I (position 9, number 9) are both odd numbers.
- K (position 11, number 11) and F (position 6, number 6) are both even numbers.
- B (position 2, number 2) is an odd number.
- W (position 23, number 23) is an even number.

Solution:
- Based on the observations and analysis, we can conclude that the next letter in the series should have a position that is 1 less than the previous letter, a number that is 3 less than the previous letter, and an odd number.
- From the given options, only option 'B' (Q) satisfies these conditions.
- Therefore, the correct option to fill in the blank and complete the series is 'Q'.

Explanation:
- The series starts with 6 and each subsequent number is obtained by multiplying the previous number by a certain factor and then adding a specific value.
- The pattern in the given series is:
- 6 x 1 + 3 = 9
- 9 x 1 + 6 = 15
- 15 x 1 + 12 = 27
- 27 x 1 + 24 = 51
- To find the next number, we will continue the pattern:
- 51 x 1 + 48 = 99
- Therefore, the missing number in the series is 99.
- Hence, the correct answer is option A) 99.

Finding the Missing Letter-Cluster in Series

Given series: BECD, FIGH, KNLM, ?, XAYZ

We need to find the missing letter-cluster in the series.

Approach:

On observing the given series, we can notice that:

- The first letter of each letter-cluster is alphabetically increasing by 1. i.e. B (2) → F (6) → K (11) → ?
- The second letter of each letter-cluster is alphabetically decreasing by 1. i.e. E (5) ← I (9) ← N (14) ← ?
- The third letter of each letter-cluster is alphabetically increasing by 1. i.e. C (3) → G (7) → L (12) → ?
- The fourth letter of each letter-cluster is alphabetically decreasing by 1. i.e. D (4) ← H (8) ← M (13) ← ?
- The first and the fourth letters of each letter-cluster are separated by two letters in alphabetical order. i.e. B, D, F, H, K, M, ?, X, and Z.

Using the above observations, we can find the missing letter-cluster as follows:

- The first letter of the missing letter-cluster should be the next alphabetically increasing letter after K, which is ‘L’.
- The second letter of the missing letter-cluster should be the next alphabetically decreasing letter after N, which is ‘M’.
- The third letter of the missing letter-cluster should be the next alphabetically increasing letter after L, which is ‘M’.
- The fourth letter of the missing letter-cluster should be the next alphabetically decreasing letter after M, which is ‘N’.

Hence, the missing letter-cluster is ‘QTRS’, which is option (D).

Pattern Analysis:
The given series follows a specific pattern where each term is the sum of the previous two terms.

Calculating the Series:
0 + 2 = 2
2 + 3 = 5
3 + 5 = 8
5 + 8 = 13
10 + 13 = 23
18 + 23 = 41
33 + 41 = 74
61 + 74 = 135
112 + 135 = 247

Identifying the Missing Number:
Therefore, the next number in the series should be the sum of 135 and 112, which is 247.

Answer:
Therefore, the correct option to fill in the blank and complete the series is 206 (247).

**Series Analysis:**

Let's analyze the given series step by step to identify the pattern and find the missing term.

1. **Step 1:** The series starts with the number 3.
2. **Step 2:** From 3, 1 is added to get the next number, which is 4.
3. **Step 3:** From 4, 1 is added to get the next number, which is 5.
4. **Step 4:** From 5, 1 is added to get the next number, which is 6.
5. **Step 5:** From 6, a difference of 3 is added to get the next number, which is 9.
6. **Step 6:** From 9, 1 is added to get the next number, which is 10.
7. **Step 7:** From 10, 1 is added to get the next number, which is 11.
8. **Step 8:** From 11, 1 is added to get the next number, which is 12.
9. **Step 9:** From 12, a difference of 3 is added to get the next number, which is 15.

**Pattern:**

From the analysis of the given series, we can observe the following pattern:

- The series consists of two sub-patterns:
- In the first sub-pattern, 1 is added consecutively to each term.
- In the second sub-pattern, a difference of 3 is added consecutively to each term.

**Finding the Missing Term:**

To find the missing term in the series, we need to continue applying the pattern.

- From 15, a difference of 3 will be added to get the next term.
- 15 + 3 = 18

Therefore, the missing term in the series is 18.

**Conclusion:**

The term that will come next in the given series is 18, which corresponds to option D.

Understanding the Series
To solve the given letter series, we need to identify the pattern in the sequence. The series provided is:
fgg ______ gff ______ f ______ gfg ______ fgf
Identifying the Pattern
- The series alternates between 'f' and 'g' in various combinations.
- Observing the entries before the gaps:
- The first part is "fgg", followed by "gff".
- The third part shows "f" which indicates a continuation of the 'f' and 'g' pattern.
Analyzing the Gaps
1. First Gap: After "fgg", the next sequence is "gff". To maintain the pattern, we can add "f" following the first gap.
2. Second Gap: After "gff", there is another 'f' which suggests that this gap should contain a 'g' to align with the existing 'g' and 'f' pattern.
3. Third Gap: The third gap follows a single 'f', indicating that it should contain 'g' next to it, following the established pattern.
4. Fourth Gap: The fourth gap follows "gfg". This suggests that we can place another 'f' here to complete the pattern.
Completing the Series
By filling in the gaps with "fb" in the first gap, "g" in the second, "g" in the third, and "f" in the last gap, we create:
fggf gffg f gfgf fgf
The complete sequence reads as:
fggf gffg f gf gfg
Thus, the correct set of letters to complete the series is option A: fggf.
Conclusion
In summary, recognizing the alternating pattern of 'f' and 'g' allowed us to logically deduce the missing letters, leading to the correct completion of the letter series.