Question

Find the first four terms of the sequence given by the following.
4,=(-1)".31%, n=1, 2, 3, ...

Answer 1

The first term of the sequence is:

• a₁ = -3

• a₂ = 12

• a₃ = -27

• a₄ = 48

Explanation:

Given the sequence

aₙ = (-1)ⁿ · 3n²

substituting n = 1 to determine the first term

a₁ = (-1)¹ · 3(1)²

a₁ = (-1)¹ · 3(1)²

Applying the exponent rule:
`a^1=a`

a₁ = -1 · 3(1)

a₁ = -1 · 3

a₁ = -3

substituting n = 2 to determine the 2nd term

a₂ = (-1)² · 3(2)²

a₂ = 1 · 3(4)

a₂ = 12

substituting n = 3 to determine the 3rd term

a₃ = (-1)³ · 3(3)²

a₃ = -1 · 3(9)

a₃ = -1 · 27

a₃ = -27

substituting n = 4 to determine the 4th term

a₄ = (-1)⁴ · 3(4)²

a₄ = 1 · 3(16)

a₄ = 1 · 48

a₄ = 48

Therefore, the first term of the sequence is:

• a₁ = -3

• a₂ = 12

• a₃ = -27

• a₄ = 48