Assume that the sequence is defined recursively. Find the first four terms of the sequence.

Question

a₁=6 and a_n+1=ka_n

Answer 1

 

Hi Shelby,

 

From a_n+1 = ka_n, we get

 

     a_n+1/a_n = k

 

which means the ratio of two consecutive terms is k.

 

So, the general equation for the sequence is

 

     a_n = k^n-1a₁

 

         = 6k^n-1

 

     a₁ = 6

 

     a₂ = 6k

 

     a₃ = 6k²

 

     a₄ = 6k³

 

     a₅ = 6k⁴

 

     ...