In the number series 141, 137, 146, 130, 155, 119, what is the next term in the sequence?

Introduction:
This is a number series question that checks your pattern recognition skills. You are given a sequence of six numbers and must determine the rule governing the changes in order to predict the next term correctly.

Given Data / Assumptions:

• Series: 141, 137, 146, 130, 155, 119, ?
• We assume there is a consistent arithmetic pattern.
• We must find the missing next number.

Concept / Approach:
For such series, we usually examine the differences between consecutive terms. If those differences themselves follow a recognizable pattern, we can extend that pattern to find the next term. Sometimes differences might be squares, cubes, alternating sequences, or follow some other simple rule.

Step-by-Step Solution:
Step 1: Compute consecutive differences. 137 - 141 = -4. 146 - 137 = +9. 130 - 146 = -16. 155 - 130 = +25. 119 - 155 = -36. So the difference sequence is: -4, +9, -16, +25, -36.
Step 2: Recognize the pattern. The absolute values are 4, 9, 16, 25, 36, which are 2^2, 3^2, 4^2, 5^2, 6^2. The signs alternate: negative, positive, negative, positive, negative.
Step 3: Predict the next difference. Following the pattern, the next square is 7^2 = 49, and the sign should now be positive (continuing the alternating pattern). So the next difference = +49.
Step 4: Find the next term. Current last term: 119. Next term = 119 + 49 = 168.

Verification / Alternative Check:
We can reconstruct the series from the starting number 141 using the pattern: 141 - 4 = 137, 137 + 9 = 146, 146 - 16 = 130, 130 + 25 = 155, 155 - 36 = 119, 119 + 49 = 168. The pattern is perfectly consistent.

Why Other Options Are Wrong:
162, 147, 182, and 152 do not arise from continuing the square difference pattern with alternating signs. Using any of these would break the established rule for the series.

Common Pitfalls:
Students often look only for simple constant differences, missing more subtle patterns such as squares, cubes, or alternating signs. It is always a good idea to examine both the size and sign of differences carefully, and to check for familiar numerical patterns like perfect squares.

Final Answer:
The next term in the series is 168.