Number series — determine the next value. Sequence: 0.5, 0.55, 0.65, 0.8, ?

Introduction / Context:
Decimal series frequently use steadily increasing increments. Here, the step sizes themselves grow in a simple arithmetic fashion. Recognizing the step pattern yields the next term quickly and accurately.

Given Data / Assumptions:

• Sequence: 0.5, 0.55, 0.65, 0.8, ?
• We check consecutive differences.
• Assume a simple incremental pattern across steps.

Concept / Approach:
Compute differences: 0.55 − 0.5 = 0.05; 0.65 − 0.55 = 0.10; 0.8 − 0.65 = 0.15. The increases are 0.05, 0.10, 0.15 — a clear arithmetic sequence with common difference 0.05. The next increase should be 0.20.

Step-by-Step Solution:
Identify step sizes: +0.05, +0.10, +0.15. Next step = previous step + 0.05 = 0.20. Next term = 0.8 + 0.20 = 1.0.

Verification / Alternative check:
Extending the differences gives 0.05, 0.10, 0.15, 0.20 — consistent linear growth of step size by 0.05.

Why Other Options Are Wrong:
0.9/0.95/0.82: Do not reflect a +0.20 jump from 0.8; they would imply inconsistent step sizes.

Common Pitfalls:
Averaging terms or assuming constant difference, missing the steadily increasing increments (0.05 added each time to the step).

Final Answer:
1