Question

List the first five terms of the sequence. a_(n)=(-¹ⁿ⁻¹/³ⁿ)

Answer 1

To find the first five terms of the sequence a_(n)=(-1)^(n-1)/(3^n), we calculate for each integer from 1 to 5, resulting in the terms 1/3, -1/9, 1/27, -1/81, and 1/243.

Step-by-step explanation:

The student has asked to list the first five terms of the sequence given by the formula a_(n)=(-1)^(n-1)/(3^n).

1. For n=1: a_1 = (-1)^(1-1)/(3^1) = 1/3
2. For n=2: a_2 = (-1)^(2-1)/(3^2) = -1/9
3. For n=3: a_3 = (-1)^(3-1)/(3^3) = 1/27
4. For n=4: a_4 = (-1)^(4-1)/(3^4) = -1/81
5. For n=5: a_5 = (-1)^(5-1)/(3^5) = 1/243

The first five terms of the sequence are 1/3, -1/9, 1/27, -1/81, and 1/243.