Question

How do you find the explicit formula for the following sequence 1/3,2/9,4/27,8/81,16/243......?

Answer 1

`a_n=1/3*(2/3)^n`

Explanation:

`a_0=1/3`
`a_1=a_0*2/3=2/9`
`a_2=a_1*2/3 = a_0*(2/3)^2 =4/27`
`a_3=a_2*2/3=a_0*(2/3)^3=8/81`
`a_4=a_3*2/3=a_0*(2/3)^4=16/243`

`color(black)("...")`

`a_n=a_0*(2/3)^n = 1/3*(2/3)^n`