Answer:
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
