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      Question

      A sequence {Uₙ} is defined as: I) U₁ = a (a

      is a real constant) II) For every n ≥ 2: Uₙ = Uₙ₋₁ + (4n − 3) It is known that U₃ + U₅ = 70. What is the value of U₆?
      A 28 Correct Answer Incorrect Answer
      B 63 Correct Answer Incorrect Answer
      C 71 Correct Answer Incorrect Answer
      D 42 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Write the first few terms in terms of a. U₁ = a For n = 2: U₂ = U₁ + (4×2 − 3) = a + 5 For n = 3: U₃ = U₂ + (4×3 − 3) = (a + 5) + 9 = a + 14 For n = 4: U₄ = U₃ + 13 = (a + 14) + 13 = a + 27 For n = 5: U₅ = U₄ + 17 = (a + 27) + 17 = a + 44 For n = 6: U₆ = U₅ + 21 = (a + 44) + 21 = a + 65 Given: U₃ + U₅ = (a + 14) + (a + 44) = 2a + 58 = 70 So: 2a = 70 − 58 = 12 a = 6 Then: U₆ = a + 65 = 6 + 65 = 71

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