Discussion
The sequence below breaks off before its final term. Identify the pattern, then choose the number that belongs at the question mark.
1, 9, 25, 49, ?
Answer: C
Correct answer: 81
The gaps are 8, 16, 24, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is the square of an odd number: position 1 gives 1 and position 4 gives 49. The next position is 5, which gives 81. As a check, the same rule applied to the earlier positions reproduces 1, 9, 25, 49 exactly, so it accounts for every term shown and not merely the last. Subtracting one from each square gives numbers that factorise neatly, which is sometimes the easier way to see the pattern.
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