Question

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​

Answer 1

B

Explanation:

Given the recurrence formula

`a_(n)` = - 3
`a_(n-1)` - 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