Official Guide Explanation:
Problem Solving #146




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Solution and Metadata

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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