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If a₁ = 7 and aₙ = -4aₙ₋₁ + n then find the value of a₅

User Li
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Final answer:

To find a5 for the recursive sequence with a1 = 7 and an = -4an-1 + n, each term up to the fifth must be calculated sequentially. The value of a5 is found to be 1701.

Step-by-step explanation:

The student is asking to find the value of a5 given the recursive sequence where a1 = 7 and an = -4an-1 + n. To find the fifth term, a5, we need to calculate the terms that come before it since it's a recursive sequence.

  1. a1 is given as 7.
  2. To find a2, plug n = 2 into the recursion: a2 = -4(7) + 2 = -28 + 2 = -26.
  3. Next, a3 = -4(-26) + 3 = 104 + 3 = 107.
  4. Then, a4 = -4(107) + 4 = -428 + 4 = -424.
  5. Finally, a5 = -4(-424) + 5 = 1696 + 5 = 1701.

Therefore, the value of a5 in the sequence is 1701.

User Surajz
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