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## Official Guide Explanation:Problem Solving #146

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.

Question: 146
Page: 172
Difficulty: 7 (Very Difficult)
Category 1: Algebra > Functions > Sequences

Explanation: In the given sequence, the value of each term (xn) depends on the values of the two preceding terms (xn - 1 and xn - 2). Thus, to find the third term (x3), we need to know the first and second term. However, we're given the "zero'th" and first terms. With those two terms, we can find the second term; from there, we can find the third term.

First, the second term:

x2 = 2x1-(1/2)(x0)

= 2(2) - (1/2)(3) = 4 - (3/2) = 2(1/2)

Now, the third term:

x3 = 2x2-(1/2)(x1)

= 2(2(1/2)) - (1/2)(2) = 5 - 1 = 4, choice (C).

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