Multiple choice

In a sequence where each term is the sum of the squares of its two preceding terms (i.e. an = a2n - 1 + a2n - 2), the first two terms are a1 = 1 and a2 = 2. What is the value of a4?

  1. 21

  2. 29

  3. 41

  4. 49
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B Correct answer
Explanation

Given a1=1, a2=2. a3 = a2^2 + a1^2 = 2^2 + 1^2 = 5. a4 = a3^2 + a2^2 = 5^2 + 2^2 = 25 + 4 = 29.

AI explanation

Using the given recursive formula, we first find a3 = 1^2 + 2^2 = 1 + 4 = 5. We then apply the same method to find the fourth term, which is a4 = 2^2 + 5^2 = 4 + 25 = 29. The result is 29.

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