Question

What is the formula of this sequence? 8; 4; 2; 1; 1/2; 1/4; 1/8; 1/16

Answer 1

Notice the following pattern,

`\begin{gathered} 8=2^3,4=2^2,2=2^1,0=2^0 \\ (1)/(2)=2^(-1),(1)/(4)=(1)/(2^2)=2^(-2),... \end{gathered}`

Therefore, the given sequence can be rewritten as shown below

`8,4,2,1,(1)/(2),(1)/(4),(1)/(8),(1)/(16),...=2^3,2^2,2^1,2^0,2^(-1),2^(-2),2^(-3),2^(-4),...`

Thus, the formula is

`a_n=2^(4-n),n\ge1`

The n-th term of the sequence is given by 2^(4-n) (n=1,2,3,...)