Karan looks at the sequence 1, 4, 9, 16 and notices each number is 3 more than the last near the…

Why

Karan did something every good mathematician starts with — he looked for a rule in the gaps between numbers, and near the start that rule really does look like "add 3." The mistake is trusting that rule to keep going without checking whether the GAP ITSELF is changing. Look closer: 1 to 4 is +3, but 4 to 9 is +5, and 9 to 16 is +7 — the gap is growing by 2 each time, not staying fixed at 3. Following that real pattern, the next gap should be +9, making the next number 16+9 = 25, not 19. These numbers are actually 1², 2², 3², 4² — square numbers — and squares grow by bigger and bigger jumps, never a constant one. Diya is right: the real answer is 25, not 19, and the fix is never to trust a pattern from two or three terms alone — extend it one more step and see if your rule survives.