Official Guide Explanation:
Problem Solving #D03




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Solution and Metadata

Question: D03
Page: 20
Difficulty: 7 (Very Difficult)
Category 1: Algebra > Functions > Sequences

Explanation: First, make sure that you understand how the sequence works. In more language, each term (an) is the average of the previous two terms (an - 1 and an - 2). So, to determine the third term, we'd need to know the first and second terms, then find the average of those two terms.

To find the sixth term, we need to know the fifth term and the fourth term. The question gives us the fifth term, but not the fourth term. However, we're given the third term. Since the fifth term is the average of the third and fourth terms, we can use the two given terms to find the fourth term:

a5 = ((a4 + a3)/2)

20 = ((a4 + 4)/2)

40 = a4 + 4

a4 = 36

Now that we know the fourth term, we can calculate the sixth term:

a6 = ((a5 + a4)/2) = ((20 + 36)/2) = (56/2) = 28

Choice (E) is correct.

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