Discussion
A consistent rule produced every one of the numbers below. Settle on the rule the terms obey and give the next number.
14, 30, 46, 62, ?
Answer: B
Correct answer: 78
Every gap is the same: the differences run 16, 16, 16, so the common difference is 16. Applying it once more to the final term, 62 + 16 gives 78. As a check, subtracting 16 from the answer returns 62, the term before it, and repeating that recovers the whole series. A series and its differences can both be regular, and identifying which is regular decides the family.
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