Choose the correct alternative that will continue the same pattern and replace x in the series: 1.5, 1.55, 1.65, 1.8, x

Introduction / Context:
This series question involves decimal numbers and gradually increasing differences. Such problems test attention to fractional increments and the ability to see patterns in non integer changes. We are asked to determine which value of x continues the pattern in the sequence 1.5, 1.55, 1.65, 1.8, x.

Given Data / Assumptions:
- Sequence: 1.5, 1.55, 1.65, 1.8, x.- Only one term, x, is unknown.- Differences between terms are small and positive, suggesting an additive pattern.

Concept / Approach:
To solve such decimal series, the easiest method is to compute the difference between consecutive terms and see whether those differences follow their own simple pattern. Frequently, they increase or decrease by a constant amount. Recognising a pattern in the differences allows us to predict the next difference and hence the next term in the series.

Step-by-Step Solution:
- From 1.5 to 1.55: 1.55 - 1.5 = 0.05.- From 1.55 to 1.65: 1.65 - 1.55 = 0.10.- From 1.65 to 1.8: 1.8 - 1.65 = 0.15.- The differences are: 0.05, 0.10, 0.15. Each time, the increment increases by 0.05.- Therefore, the next difference should be 0.20.- So x = 1.8 + 0.20 = 2.0.

Verification / Alternative check:
- With x = 2.0, the sequence of differences becomes 0.05, 0.10, 0.15, 0.20, which is an arithmetic progression with common difference 0.05.- The resulting series 1.5, 1.55, 1.65, 1.8, 2.0 is smooth and consistent.

Why Other Options Are Wrong:
- 1.95, 1.85, 2.05 and 1.9 do not give a difference of 0.20 from 1.8, and they break the steadily increasing difference pattern.- For instance, 1.95 would give a difference of 0.15 again instead of 0.20, which fails to continue the growth in the increments.

Common Pitfalls:
- Misreading decimal values (for example mixing 0.05 and 0.5) can lead to incorrect differences.- Some candidates may stop after recognising that the series increases, without noticing that the increments themselves are increasing in a systematic way.- Rounding the values too roughly can hide the true underlying pattern.

Final Answer:
The next difference should be 0.20, so the missing term is 1.8 + 0.20 = 2.0.