Question

What is the next number in the sequence below?
7, 11, 18, 30, 50, ____

• A. 83
• B. 84
• C. 85
• D. 86

Hint:

For complex number series, always calculate the first differences. If you don't see a pattern, calculate the second differences. Often, a simple arithmetic, geometric, or Fibonacci-like pattern will reveal itself at this second level.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks for the next term in the given numerical sequence.
Step 2: Key Formula or Approach:
When the difference between terms is not constant, we should look for a pattern in the differences themselves (a second-level difference) or a recursive relationship.
Step 3: Detailed Explanation:
Let's write down the sequence and find the difference between consecutive terms.
Sequence: 7, 11, 18, 30, 50, ?
First-level differences:
- \(11 - 7 = 4\)
- \(18 - 11 = 7\)
- \(30 - 18 = 12\)
- \(50 - 30 = 20\)
The differences are: 4, 7, 12, 20. There is no obvious simple pattern here.
Let's find the differences of these differences (second-level differences):
- \(7 - 4 = 3\)
- \(12 - 7 = 5\)
- \(20 - 12 = 8\)
The second-level differences are: 3, 5, 8.
This sequence (3, 5, 8) has a clear pattern. Each term is the sum of the previous two terms (similar to a Fibonacci sequence): \(3 + 5 = 8\).
The next term in this second-level difference sequence would be \(5 + 8 = 13\).
Now we can work our way back up to find the next term in the original sequence.
- The next first-level difference will be the last one (20) plus the next second-level difference (13): \(20 + 13 = 33\).
- The next term in the original sequence will be the last term (50) plus this new difference (33): \(50 + 33 = 83\).
The sequence would continue as: 7, 11, 18, 30, 50, 83.
Step 4: Final Answer:
The next number in the sequence is 83. This corresponds to option (A).