Recursive formula for the sequence

Question

n in the table is 1-4 and a_{2 is 405, 135, 45, and 15}

Answer 1

405, 135, 45, 15 is geometric with common ratio 1/3.

 

     In other words, 135/405 = 45/135 = 15/45 = 1/3.

 

a₁ = 405

 

a₂ = 405(1/3) = (1/3)a₁ = 135

 

a₃ = 135(1/3) = (1/3)a₂ = 45, etc

 

Recursive formula:  a₁ = 405

                             a_n = (1/3)a_n-1 , for n≥2