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In the expansion (1 + x²)² * (1 + x)ⁿ = sumₖ₌₀ⁿ⁺⁴ aₖ * x^k, the coefficients a1, a2, a3 are in arithmetic progression. Which of the following values of n is NOT possible?
- 1
- 2
- 3
- 4
Correct answer: 1
Solution
The AP condition reduces to n³ - 9n² + 26n - 24 = 0, which factors as (n-2)(n-3)(n-4) = 0; so n = 2, 3, 4 all satisfy the AP condition, meaning n = 1 is the value that does NOT satisfy it and hence is NOT possible.
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