How do you find the first four terms of the sequence defined by the formula a₁ = 1 and aₙ = 4 aₙ₋₁?

To find the first four terms of the sequence defined by a₁ = 1 and a_n = 4 a_n-1, we will start by computing each term step by step:

1. First term (a₁): By the given condition, we have:
   • a₁ = 1
2. Second term (a₂): Using the formula a_n = 4 a_n-1, we calculate:
   • a₂ = 4 a₁ = 4 × 1 = 4
3. Third term (a₃): Now we compute:
   • a₃ = 4 a₂ = 4 × 4 = 16
4. Fourth term (a₄): Finally, we find:
   • a₄ = 4 a₃ = 4 × 16 = 64

Thus, the first four terms of the sequence are:

• a₁ = 1
• a₂ = 4
• a₃ = 16
• a₄ = 64

In summary, the first four terms are: 1, 4, 16, and 64.