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
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories