Find the first five terms of the sequence in which a1 = 6 and an = -3an-1 - 12, if n _> 2.
a. -30, 78, -246, -2190
b. 6, -30, 78, -246 , 726
c. 6, 6, -30, 78 -246
d. -15, -18, -21, -27

B

Step-by-step explanation:

Given the recurrence formula

= - 3 - 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