Answer:
The first term of the sequence is:
- a₁ = -3
- a₂ = 12
- a₃ = -27
- a₄ = 48
Step-by-step 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:
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