Discussion
One entry is missing from the sequence set out below. Work out the rule and supply the missing number.
4374, 1458, 486, 162, ?
Answer: B
Correct answer: 54
The terms shrink by a constant factor rather than by a constant amount: 4374 over 1458 is 3, and the same holds for every neighbouring pair, so each term is the previous one divided by 3. Dividing the last term, 162 over 3 is 54. As a check, multiplying the answer by 3 returns 162, the term before it. The terms of a halving series must eventually reach a number that will not divide evenly, which limits how long such a series can run.
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