Question

Find the first five terms of each sequence.

aₙ = -3(aₙ₋₁) - 1 where aₙ=-5 A) -5, -14, -41, -122, -365
B) -5, -16, -47, -140, -419
C) -5, -8, -11, -14, -17
D) -5, -11, -23, -47, -95

Answer 1

The first five terms of the sequence defined by a_n = -3(a_n-1) - 1 and a_1 = -5 are -5, 14, -43, 128, and -385.

Step-by-step explanation:

The student is asking to find the first five terms of the sequence defined by the recursive formula an = -3(an-1) - 1 with the first term a1 = -5. To find these terms, we'll apply the formula successively, starting with a1.

1. a1 = -5 (given)
2. a2 = -3(a1) - 1 = -3(-5) - 1 = 15 - 1 = 14
3. a3 = -3(a2) - 1 = -3(14) - 1 = -42 - 1 = -43
4. a4 = -3(a3) - 1 = -3(-43) - 1 = 129 - 1 = 128
5. a5 = -3(a4) - 1 = -3(128) - 1 = -384 - 1 = -385

Therefore, the first five terms of the sequence are: -5, 14, -43, 128, -385.