If a sub 1 4 and a sub k plus 15a sub k for k0 then a sub n

If a sub 1 =4 and a sub k plus 1=5a sub k for k>0 then a sub n =5^4

Solution

The question is not clear. I Better take picture of it and post. I think that \"sub\" here refers to a subscript. So I could picture the question as follows:

a₁ = 4 ; a_k+1 = 5*a_k for k>0

And what exactly are you asking in your question? Do you want a proof of something or find the value of n?

a₂ = 5*a₁ = 5*4 = 20

a₃ = 5*a₂ = 5*20 = 100 = 5² x 4

a₄ = 5*a₃ = 5*100 = 5³ x 4

As seen from the above trend, a_n = 5^n-1 x 4

If the question is something else do tell me.