Mathematics — Standard (041) — CBSE Class 10 board question

Option D: $1^2, 3^2, 5^2, 7^2, \ldots$ i.e., $1, 9, 25, 49, \ldots$ is not an AP, as the differences $9-1=8$, $25-9=16$, $49-25=24$ are not equal.

Check each option by finding consecutive differences:

• A: $d = \frac{1}{2}$ ✓ (AP)
• B: $d = -2$ ✓ (AP)
• C: $\sqrt{2}, \sqrt{8}=2\sqrt{2}, \sqrt{18}=3\sqrt{2}$ → $d = \sqrt{2}$ ✓ (AP)
• D: $1, 9, 25, 49$ → differences 8, 16, 24 — not constant ✗ (NOT an AP)

The textbook (Exercise 5.1, Q4, xiv) confirms $1^2, 3^2, 5^2, 7^2$ is an AP — but that question asks to find common difference if it is one. Actually, verifying shows it is not an AP since differences are unequal. Option D is the correct answer.