Find the fifth term of the sequence given by the recursive formula

t1 = 4 and tn = 2tn-1 - 5

The fifth term is - 11

Step-by-step explanation:

t₁ = 4

tₙ = 2tₙ₋₁ - 5

TO calculate the fifth term of the sequence, we will follow the steps below;

t₁ = 4

tₙ = 2tₙ₋₁ - 5

substitute for n=2 in the recursive formula and then solve

t₂ = 2t₂₋₁ - 5

t₂ = 2t₁ - 5

t₂ = 2 (4) - 5

t₂ = 8-5

t₂ = 3

substitute for n=3 in the recursive formula and then solve

t₃ = 2t₃₋₁ - 5

t₃ = 2t₂ - 5

t₃ = 2 (3) - 5

t₃ = 6 - 5 = 1

t₃ = 1

substitute for n = 4 in the recursive formula and then solve

t₄ = 2t₄₋₁ - 5

t₄ = 2t₃ - 5

t₄=2 (1) - 5 = 2 - 5 = - 3

t₄ = - 3

substitute for n = 5 in the recursive formula and then solve

t₅ = 2t₅₋₁ - 5

t₅ = 2t₄ - 5

t₅ = 2 (-3) - 5

t₅ = - 6-5 = - 11

t₅ = - 11

The fifth term is - 11