Number Series

To solve the problem, we need to identify the pattern in the number series: 5, 11, 24, 51, ?, 213.

1. Observing the Pattern:
Let’s examine the differences between consecutive terms:

11 − 5 = 6
24 − 11 = 13
51 − 24 = 27
? − 51 = ?
213 − ? = ?

2. Analyzing the Differences:
Now, look at the pattern in the differences:

6, 13, 27
Next difference? Let’s analyze this:
From 6 to 13: +7
From 13 to 27: +14
Pattern of adding (7, 14, ...), appears to double.
So, next difference = 27 + 28 = 55

3. Calculating the Missing Number:
Now add the next difference to the last known number:

51 + 55 = 106

4. Confirming the Pattern:
Final term is 213. Check the difference between 213 and 106:

213 − 106 = 107
Previous difference was 55; if pattern of doubling continues:
Next difference = 55 + 52 = 107 → which matches!

Final Answer:
The missing number in the series is 106.

Solution:

To determine the next number in the series , we first identify the pattern in the sequence.

Let's examine the differences between consecutive terms:

• From to :
• From to :
• From to :
• From to :

The differences between the terms are . This sequence of differences is increasing by each time.

Continuing this pattern, the next difference should be:

Thus, the next term in the series can be found by adding to :

Hence, the next number in the series is 42.

The given series is: 2, 4, 8, 16, ?
Each term is multiplied by 2 to get the next term: So, the next term will be: Final answer Answer:

To solve the problem, we need to find the pattern in the series and identify the missing term.

1. Understanding the Concepts:

- Number Series: A sequence of numbers that follow a specific pattern.
- Pattern Recognition: Identify the rule governing the progression from one term to the next.

2. Given Series:

3, 6, 11, 18, 27, ?

3. Analyzing the Differences:

Calculate the differences between consecutive terms:
6 - 3 = 3
11 - 6 = 5
18 - 11 = 7
27 - 18 = 9

4. Identify the Pattern:

The differences form the sequence: 3, 5, 7, 9
This is an increasing sequence of odd numbers, increasing by 2 each time.
The next difference should be 11.

5. Calculate the Missing Term:

Last known term = 27
Next term = 27 + 11 = 38

Final Answer:

The missing term in the series is 38.

To solve the problem, we need to identify the pattern in the number series and find the next number.

1. Understanding the Concepts:

- Number Series: A sequence of numbers following a certain rule.
- Pattern Recognition: Analyze the differences or formulas generating the series.

2. Given Series:

2, 6, 12, 20, 30, ?

3. Analyzing the Pattern:

Look at the pattern in the terms:

• 2 = 1 × 2
• 6 = 2 × 3
• 12 = 3 × 4
• 20 = 4 × 5
• 30 = 5 × 6

So, the nth term =

4. Calculate the Next Term:

For :

Final Answer:

The next number in the series is 42.