What is the tenth term of the sequence described by the following f1 = -2, tn =3tn-1

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

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