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## Official Guide Explanation:

Problem Solving #228

**Background**

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Review (12th ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

Click here for an example of the PDF booklets. Click here to purchase a PDF copy.

**Solution and Metadata**

**Question****: 228**

Page: 185

Difficulty: **7** (Very Difficult)

Category 1: Algebra > Functions > Sequences

Category 2: Algebra > Exponents >

**Explanation:** Another way to phrase the definition of "arithmetic sequence" is to say that the numbers in such a sequence are equally spaced. For instance, they could be consecutive integers, consecutive evens, or consecutive multiples of 7. To look at each of the statements individually:

I. By doubling each number, you double the distance between them, but the distance between each one is still the same. For instance, if a sequence is {1, 2, 3}, doubling each number results in {2, 4, 6}, still equally spaced.

II. Subtracting 3 from each number may change each number, but it doesn't change the amount of space between them. For instance, the sequence {4, 5, 6} becomes {1, 2, 3}.

III. In this case, the numbers change, and the distance between them changes as well. Instead of a consistent amount between numbers, the distance grows with each number. for example, the sequence {2, 3, 4} would become {4, 9, 16}, with differences of 5 and 7 between them--not a constant.

Thus, I and II are arithmetic sequences, while III is not. That makes (D) the correct answer.

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