212k views
5 votes
What is the formula of this sequence? 8; 4; 2; 1; 1/2; 1/4; 1/8; 1/16

1 Answer

1 vote

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,...)

User Darren Cook
by
7.0k points