Arithmetic Sequence

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An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant. If the list of letters shown above is an arithmetic sequence, which of the following must also be an arithmetic sequence?

I.

II.

III.

Review: Arithmetic Sequence


Explanation

In this question, we can translate the definition of an arithmetic sequence into an example. Say the constant in question is 4. Then the numbers from n on will be . Then, Roman numeral I gives . That's still an arithmetic sequence, just with a different starting number, now 3n, and a bigger constant, now 12. It's only one example, but I can see it will be true for any constant. So I is in. Given the answer choices, that means we won't have to evaluate III. As for II, this will just change the constant from 4 to 2, so that will be an arithmetic sequence.

The correct answer is (D).


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