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Which of these is the correct statement about the AP 5, 5, 5, 5, …?

Class 10Arithmetic ProgressionsAlgebra — Sequences
  • AIt is an AP with common difference 0.
  • BIt is not an AP because the terms do not change.
  • CIt is a geometric progression only.
  • DIts common difference is 5.

Step-by-Step Solution

A constant sequence has the same difference (0) between consecutive terms, so it qualifies as an AP with d = 0.
Answer: A) It is an AP with common difference 0.

Key idea: Recognising an AP

A sequence is an AP iff the difference of consecutive terms is constant.

**Test**: Compute a₂ − a₁ and a₃ − a₂. If they're equal, it's likely an AP — verify with a₄ − a₃.

**Examples**:
- 4, 7, 10, 13: differences 3, 3, 3 → AP, d = 3.
- 1, 4, 9, 16: differences 3, 5, 7 → NOT an AP (these are squares).
- 5, 5, 5, 5: differences 0, 0, 0 → AP with d = 0 (a constant sequence is an AP).
- 2, 6, 12, 20: differences 4, 6, 8 → NOT an AP.

The common difference d can be positive (increasing AP), negative (decreasing AP), or zero (constant AP).

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