Choose the correct alternative that will continue the same pattern and replace x in the series: 1, 2, 5, 10, 25, 50, x, 250

Introduction / Context:
This number series question uses alternating multiplication factors and is typical of reasoning tests where candidates must detect a pattern in how each term is generated from the previous one. The sequence 1, 2, 5, 10, 25, 50, x, 250 shows smooth growth and suggests a combination of doubling and multiplying by a fraction like 2.5.

Given Data / Assumptions:
- Sequence: 1, 2, 5, 10, 25, 50, x, 250.- Only one term, x, is missing.- Each term is strictly greater than the previous term.

Concept / Approach:
A good approach is to compute ratios of successive terms. If the ratio alternates between two values, we can reconstruct the rule and extend the series. The presence of values like 5, 10, 25, 50 and 250 also hints at common factors of 2 and 5, guiding us toward multipliers such as 2 and 2.5.

Step-by-Step Solution:
- From 1 to 2: 2 / 1 = 2 (multiplied by 2).- From 2 to 5: 5 / 2 = 2.5 (multiplied by 2.5).- From 5 to 10: 10 / 5 = 2 (multiplied by 2).- From 10 to 25: 25 / 10 = 2.5 (multiplied by 2.5).- From 25 to 50: 50 / 25 = 2 (multiplied by 2).- We see the pattern: multiply alternately by 2 and 2.5.- After 50, we should apply the next factor, which is 2.5.- So x = 50 * 2.5 = 125.- After that, the next factor would be 2, giving 125 * 2 = 250, which matches the last term.

Verification / Alternative check:
- Rewriting the full pattern: 1 * 2 = 2, 2 * 2.5 = 5, 5 * 2 = 10, 10 * 2.5 = 25, 25 * 2 = 50, 50 * 2.5 = 125, 125 * 2 = 250.- The alternating factors 2 and 2.5 are confirmed throughout.

Why Other Options Are Wrong:
- 75, 150, 100 and 60 do not equal 50 multiplied by 2.5 and therefore fail to preserve the alternating pattern.- In particular, if x were 150 or 100, the final step to reach 250 would require a different multiplier, breaking the neat alternating rule.

Common Pitfalls:
- Some candidates only check differences (1, 3, 5, 15, 25, etc.), which look irregular and can hide the true multiplicative structure.- It is easy to overlook 2.5 as a multiplier because it is not an integer, even though it fits the ratio perfectly.- Trying to force a single constant ratio instead of considering alternating ratios can also cause confusion.

Final Answer:
Using the alternating pattern of multiplying by 2 and then by 2.5, the missing term is 50 * 2.5 = 125.