Question

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

Answer 1

The sequence is a Geometric Sequence.

The formula of a geometric sequence is given to be:

`a_n=a_1r^(n-1)`

where a₁ is the first term of the sequence, and r is the common ratio.

The common ratio is calculated to be:

`\begin{gathered} r=(a_2)/(a_1)=(4)/(8) \\ r=(1)/(2) \end{gathered}`

and the first term is:

`a_1=8`

Therefore, the formula for the nth term is given to be:

`a_n=8((1)/(2))^(n-1)`