Question

What is the next number in the sequence below?
341, 214, 123, 62, 25, ?

• A. 6
• B. 8
• C. 9
• D. 7

Hint:

For number series questions, if you don't spot a simple arithmetic or geometric progression, immediately test for patterns like \(n^2\), \(n^2 \pm k\), \(n^3\), or \(n^3 \pm k\), where 'k' is a constant. This is a very common pattern in competitive exams.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks to find the next term in a given numerical sequence by identifying the underlying pattern.
Step 2: Key Formula or Approach:
When the differences between consecutive terms are not constant, it's useful to check for patterns related to squares or cubes of integers. We can compare each term in the sequence to nearby perfect cubes.
Step 3: Detailed Explanation:
Let's analyze the sequence: 341, 214, 123, 62, 25, ?
Let's list the cubes of consecutive integers starting from 7, as 341 is close to \(7^3\):
- \(7^3 = 343\)
- \(6^3 = 216\)
- \(5^3 = 125\)
- \(4^3 = 64\)
- \(3^3 = 27\)
- \(2^3 = 8\)
Now, let's compare these values with the terms of the sequence:
- 1st term: \(341 = 343 - 2 = 7^3 - 2\)
- 2nd term: \(214 = 216 - 2 = 6^3 - 2\)
- 3rd term: \(123 = 125 - 2 = 5^3 - 2\)
- 4th term: \(62 = 64 - 2 = 4^3 - 2\)
- 5th term: \(25 = 27 - 2 = 3^3 - 2\)
The pattern is clearly \(n^3 - 2\), where 'n' is a decreasing sequence of integers starting from 7. To find the next term, we use the next integer in the sequence, which is 2.
\[ \text{Next term} = 2^3 - 2 \] \[ \text{Next term} = 8 - 2 = 6 \] Step 4: Final Answer:
The next number in the sequence is 6. This corresponds to option (A).