What are the first three terms of the sequence defined by a1 = 3 and an = 2an – 12?

The given sequence is defined with the first term as a₁ = 3 and follows the recurrence relation a_n = 2a_n-1 – 12 for n > 1.

To determine the first three terms, we can calculate them step by step:

1. Term 1 (a₁):

   The first term is given: a₁ = 3.

2. Term 2 (a₂):

   Using the recurrence relation:

   a₂ = 2a₁ – 12 = 2(3) – 12 = 6 – 12 = -6.

3. Term 3 (a₃):

   Now we find the third term:

   a₃ = 2a₂ – 12 = 2(-6) – 12 = -12 – 12 = -24.

In summary, the first three terms of the sequence are:

• a₁ = 3
• a₂ = -6
• a₃ = -24

Thus, the first three terms of the sequence are:

3, -6, -24