Find the first five terms of the recursively defined infinite sequence. a1 = 3, ak+1 = 2ak − 5

Question

Find the first five terms of the recursively defined infinite sequence.

a₁ = 3,  a_k+1 = 2a_k − 5

a1=

a2=

a3=

a4=

a5=

Answer 1

Well, we know a₁ = 3, so we can plug it into the recursive equation to get the other 4 terms.

a₁ = 3

a₂ = 2a₁ - 5 = 2(3) - 5 = 1

a₃ = 2a₂ - 5 = 2(1) - 5 = -3

a₄ = 2a₃ - 5 = 2(-3) - 5 = -11

a₅ = 2a₄ - 5 = 2(-11) - 5 = -27