Solving the Missing Number Series

This question asks us to find the missing number in the given series: 34, 71, 108, 145, ?, 219. To solve number series problems, we need to identify the pattern or rule that connects the numbers.

Analyzing the Number Series Pattern

Let's look at the relationship between consecutive terms in the series. We can calculate the difference between each pair of adjacent numbers:

• Difference between the second term (71) and the first term (34): $71 - 34$
• Difference between the third term (108) and the second term (71): $108 - 71$
• Difference between the fourth term (145) and the third term (108): $145 - 108$

Calculating the Pattern Difference

Let's perform the subtractions:

• $71 - 34 = 37$
• $108 - 71 = 37$
• $145 - 108 = 37$

The difference between consecutive terms is consistently 37. This indicates that the pattern is adding 37 to each term to get the next term in the series. This is an arithmetic progression with a common difference of 37.

Finding the Missing Number

To find the missing number (the fifth term), we need to add the common difference (37) to the fourth term (145).

Missing Number = Fourth Term + Common Difference

Missing Number = $145 + 37$

Calculating the Missing Term Value

$145 + 37 = 182$

So, the missing number is 182.

Verifying the Pattern

Let's check if adding 37 to 182 gives the last term (219):

$182 + 37 = 219$

This matches the last term in the series, confirming that our calculated missing number is correct.

The complete series is 34, 71, 108, 145, 182, 219.

Final Answer Determination

Based on our analysis, the missing number in the series is 182.

Revision Table - Number Series Concepts

Additional Information - Types of Number Series

Number series problems can have various patterns. Some common types include:

• Arithmetic Series: Constant difference between terms (like the one in this question).
• Geometric Series: Constant ratio between terms (multiplying by a fixed number).
• Difference Series: The differences between terms follow a pattern themselves (e.g., the differences increase by a constant amount).
• Mixed Series: Involving a combination of operations (e.g., alternate addition and subtraction, or addition and multiplication).
• Fibonacci Series: Each term is the sum of the two preceding ones (e.g., 1, 1, 2, 3, 5, 8...).

Identifying the pattern often involves calculating differences, ratios, or looking for squares, cubes, or other mathematical relationships.