How do you find the first six terms of the sequence defined by the relation a_n = 7a_{n-1} – 4?

To find the first six terms of the sequence defined by the relation a_n = 7a_n-1 – 4, we first need to know the initial term of the sequence. Let’s assume the first term, a₁, is defined as:

a₁ = 1 (you could choose another value, but for this example, we’ll start with 1).

Now, we can calculate the subsequent terms using the recursive formula:

1. a₁ = 1
2. a₂ = 7 * a₁ – 4 = 7 * 1 – 4 = 3
3. a₃ = 7 * a₂ – 4 = 7 * 3 – 4 = 21 – 4 = 17
4. a₄ = 7 * a₃ – 4 = 7 * 17 – 4 = 119 – 4 = 115
5. a₅ = 7 * a₄ – 4 = 7 * 115 – 4 = 805 – 4 = 801
6. a₆ = 7 * a₅ – 4 = 7 * 801 – 4 = 5607 – 4 = 5603

Thus, the first six terms of the sequence are:

• a₁ = 1
• a₂ = 3
• a₃ = 17
• a₄ = 115
• a₅ = 801
• a₆ = 5603

Feel free to substitute a₁ with another starting point to generate a different sequence!