Official Guide Explanation:
Problem Solving #131

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Solution and Metadata

Question: 131
Page: 78
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Functions > Sequences

Explanation: The sequence notation gets complicated, but in short, it tells us that for the first k terms, each term in the set is 3 greater than the previous one. After that, each term is 3 less than the previous one. Clearly, the numbers increase for a while, then decrease at the same rate.

We know that x₀ = x_n = 0, so the sequence starts and ends at zero. x_k = 15, so since the numbers increase by 3 up to x_k, the sequence starts:

(0, 3, 6, 9, 12, 15)

0 is the 0th number in the set (x₀) so 3 is the 1st and 15 is the 5th. It will take 5 more numbers to decrease back to zero:

(0, 3, 6, 9,12, 15, 12, 9, 6, 3, 0)

There are 11 numbers in the set, but since the index numbers start counting at zero, the final number is the 10th. Thus, x_n is the same as x₁₀ , so n = 10, choice (D).

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