Question

Find the fifth term of the sequence given by the recursive formula t1 = 4 and tn = 2tn-1 - 5

Answer 1

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