Solving the Number Series Pattern

The question asks us to find the next term in the given number series: 13, 18, 28, 43, 63, ?

To solve a number series problem, we typically look for a pattern between consecutive terms. Let's examine the differences between the terms:

• Difference between the 2nd and 1st term: $18 - 13 = 5$
• Difference between the 3rd and 2nd term: $28 - 18 = 10$
• Difference between the 4th and 3rd term: $43 - 28 = 15$
• Difference between the 5th and 4th term: $63 - 43 = 20$

Let's list these differences:

$5, 10, 15, 20, \dots$

Observing the differences, we can see a clear pattern. The differences themselves form an arithmetic progression with a common difference of 5. Each subsequent difference is 5 more than the previous one.

• $10 - 5 = 5$
• $15 - 10 = 5$
• $20 - 15 = 5$

Following this pattern, the next difference in the series of differences should be $20 + 5 = 25$.

Now, to find the next term in the original series, we need to add this next difference (25) to the last term given in the series (63).

Next term = Last term + Next difference

Next term = $63 + 25$

Next term = $88$

Therefore, the number that should come in place of ? in the given series is 88.

Let's check this against the given options:

• 92
• 88
• 81
• 89

The calculated next term, 88, matches one of the options.

Revision Table: Key Learnings on Number Series

Additional Information on Number Patterns and Reasoning

Number series problems are common in aptitude and reasoning tests. They assess your ability to identify patterns and apply logical rules.

Common types of number series patterns include:

• Arithmetic Series: Constant difference between terms.
• Geometric Series: Constant ratio between terms (multiplying or dividing by a fixed number).
• Difference Series: The differences between terms follow a pattern (like the one solved above, where differences form an arithmetic series).
• Mixed Series: Involves a combination of patterns, sometimes alternating between two rules.
• Fibonacci Series: Each term is the sum of the two preceding ones (e.g., 1, 1, 2, 3, 5, 8...).
• Square/Cube Series: Terms are squares or cubes, or related to them (e.g., $n^2$, $n^2+1$, $n^3$, $n^3-1$).

Solving these problems often requires practice in recognizing various types of patterns quickly. It's useful to try calculating differences first, as it reveals many common patterns like arithmetic series or difference series based on arithmetic or geometric progressions.