Identifying the Number Series Pattern

The given number series is 60, 40, 50, ?, 180, 460. We need to find the missing number represented by the question mark ‘?’. Let's analyze the relationship between consecutive terms to find a consistent pattern.

Step-by-Step Pattern Analysis

Let's examine the operations between the terms:

• From 60 to 40: The difference is $40 - 60 = -20$. Alternatively, we can observe a multiplication pattern. $60 \times \frac{2}{3} \approx 40$. Let's explore multiplication with an addition/subtraction component. Consider multiplying by 0.5 and adding 10: $60 \times 0.5 + 10 = 30 + 10 = 40$. This works.
• From 40 to 50: The difference is $50 - 40 = +10$. Using the same potential pattern: Multiply by 1.0 and add 10: $40 \times 1.0 + 10 = 40 + 10 = 50$. This also works.
• From 50 to ?: Following the established pattern, the multiplier is increasing by 0.5 each time. So, the next multiplier should be $1.0 + 0.5 = 1.5$. Let's apply this: $50 \times 1.5 + 10 = 75 + 10 = 85$. So, the missing number is likely 85.
• From ? (85) to 180: The next multiplier should be $1.5 + 0.5 = 2.0$. Let's check: $85 \times 2.0 + 10 = 170 + 10 = 180$. This matches the series.
• From 180 to 460: The final multiplier should be $2.0 + 0.5 = 2.5$. Let's check: $180 \times 2.5 + 10 = 450 + 10 = 460$. This matches the series.

The pattern is consistent: Multiply the current term by an increasing sequence of multipliers (0.5, 1.0, 1.5, 2.0, 2.5) and then add 10 to get the next term.

Verification of the Pattern

Let's summarize the pattern application:

Conclusion

Based on the analysis, the number that should come in place of the question mark ‘?’ is 85.