Answer:
The 10th term will be:
t₁₀ = 39366
Step-by-step explanation:
Given the sequence
tₙ = -3 tₙ₋₁
Given
t₁ = -2
substitute n = 2, to determine the 2nd term
tₙ = -3 tₙ₋₁
t₂ = -3 tₙ₋₁
t₂ = -3 t₂₋₁
t₂ = -3 t₁
t₂ = -3 × -2 ∵ t₁ = -2
t₂ = 6
substitute n = 3, to determine the 3rd term
tₙ = -3 tₙ₋₁
t₃ = -3 t₃₋₁
t₃ = -3 t₂
t₃ = -3 × 6 ∵ t₂ = 6
t₃ = -18
substitute n = 4, to determine the 4th term
tₙ = -3 tₙ₋₁
t₄ = -3 t₄₋₁
t₄ = -3 t₃
t₄ = -3 × -18 ∵ t₃ = -18
t₄ = 54
substitute n = 5, to determine the 5th term
tₙ = -3 tₙ₋₁
t₅ = -3 t₅₋₁
t₅ = -3 t₄
t₅ = -3 × 54 ∵ t₄ = 54
t₅ = -162
substitute n = 6, to determine the 6th term
tₙ = -3 tₙ₋₁
t₆ = -3 t₆₋₁
t₆ = -3 t₅
t₆ = -3 × -162 ∵ t₅ = -162
t₆ = 486
substitute n = 7, to determine the 7th term
tₙ = -3 tₙ₋₁
t₇ = -3 t₇₋₁
t₇ = -3 t₆
t₇ = -3 × 486 ∵ t₆ = 486
t₇ = -1458
substitute n = 8, to determine the 8th term
tₙ = -3 tₙ₋₁
t₈ = -3 t₈₋₁
t₈ = -3 t₇
t₈ = -3 × -1458 ∵ t₇ = -1458
t₈ = 4374
substitute n = 9, to determine the 9th term
tₙ = -3 tₙ₋₁
t₉ = -3 t₉₋₁
t₉ = -3 t₈
t₉ = -3 × 4374 ∵ t₈ = 4374
t₉ = -13122
substitute n = 10, to determine the 10th term
tₙ = -3 tₙ₋₁
t₁₀ = -3 t₁₀₋₁
t₁₀ = -3 t₉
t₁₀ = -3 × -13122 ∵ t₉ = -13122
t₁₀ = 39366
Therefore, the 10th term will be:
t₁₀ = 39366
