What are the first six terms of the sequence defined by a1 = 8 and the recurrence relation an = 5an-1?

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To find the first six terms of the sequence defined by a1 = 8 and the recurrence relation an = 5an-1, we will start by calculating each term using the previous term.

  1. a1 = 8
  2. To find a2, we use the formula:

    3. a2 = 5a1

    a2 = 5 * 8 = 40

  3. a3:

    4. a3 = 5a2

    a3 = 5 * 40 = 200

  4. a4:

    5. a4 = 5a3

    a4 = 5 * 200 = 1000

  5. a5:

    6. a5 = 5a4

    a5 = 5 * 1000 = 5000

  6. a6:

    7. a6 = 5a5

    a6 = 5 * 5000 = 25000

So the first six terms of the sequence are:

  • a1 = 8
  • a2 = 40
  • a3 = 200
  • a4 = 1000
  • a5 = 5000
  • a6 = 25000

This pattern shows how rapidly the terms increase due to the multiplication by 5 at each step in the sequence.

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