List the first five terms of the sequence. a_n = (-1)^{n - 1}/6ⁿ

Solution:

Given, a_n = (-1)^{n - 1}/6ⁿ

Put n =1,

a₁ = [(-1)^{1 - 1}]/6¹ = 1/6

Put n =2,

a₂ = [(-1)^{2 - 1}]/6² = -1/36

Put n =3,

a₃ = [(-1)^{3 - 1}]/6³ = 1/216

Put n =4,

a₄ = [(-1)^{4 - 1}]/6⁴ = -1/1296

Put n =5,

a₅ = [(-1)^{5 - 1}]/6⁵ = 1/7776

Therefore,

The first five terms of the sequence are 1/6, -1/36, 1/216, -1/1296, 1/7776,...

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List the first five terms of the sequence. a_n = (-1)^{n - 1}/6ⁿ

Summary:

The first five terms of the sequence, a_n = (-1)^{n - 1}/6ⁿ are 1/6, -1/36, 1/216, -1/1296, 1/7776,...