A sequence is defined recursively by the given formulas?

Science & Mathematics by Anonymous 2018-06-25 01:34:09

Social Science

1 answer

Find the first five terms of the sequence. an = 4an − 1 + 1 and a1 = 1 can someone explain how to do these sorts of problems to me?

Anonymous

aₙ = 4aₙ₋₁ + 1 a₁ = 1 (Given) When n = 2: a₂ = 4a₁ + 1 = 4×1 + 1 = 5 When n = 3: a₃ = 4a₂ + 1 = 4×5 + 1 = 21 When n = 4: a₄ = 4a₃ + 1 = 4×21 + 1 = 85 When n = 5: a₅ = 4a₄ + 1 = 4×85 + 1 = 341