Answer:
B
Step-by-step explanation:
Given the recurrence formula
[tex]a_{n}[/tex] = - 3[tex]a_{n-1}[/tex] - 12 with a₁ = 6
To find the terms in the sequence substitute n = 2, 3, 4, 5 into the formula
a₂ = - 3a₁ - 12 = (- 3 × 6) - 12 = - 18 - 12 = - 30
a₃ = - 3a₂ - 12 = (- 3 × - 30) - 12 = 90 - 12 = 78
a₄ = - 3a₃ - 12 = (- 3 × 78) - 12 = - 234 - 12 = - 246
a₅ = - 3a₄ - 12 = (- 3 × - 246) - 12 = 738 - 12 = 726
Hence the first 5 terms of the sequence are
6, - 30, 78, - 246, 726 → B
