Respuesta :
For an arithmetic sequence, there is a common difference between the adjacent numbers. An arithmetic sequence starting with the number can be given as,
a, a+d, a+d+d+a+d+d+d,...
a,a+d, a+2d, a+3d....
Here, d is the common difference
Consider the sequence, 0.5, 2, 8, 32, 128 .Fiirst find the difference between adjacent numbers.
[tex]\begin{gathered} 2-0.5=1.5 \\ 8-2=4 \end{gathered}[/tex]So, there is no common difference between adjacent numbers. Therefore, the sequence 0.5, 2, 8, 32, 128 is not an arithmetic sequence.
A geometric sequence is given by,
[tex]a,ar,ar^2,ar^3,\ldots.[/tex]Here, each term after the first is multiplied by a common factor r.
Now, divide each term by the previous term in the sequence 0.5, 2, 8, 32, 128 and find if there is any common factor.
[tex]\begin{gathered} \frac{2}{0.5}=4 \\ \frac{8}{2}=4 \\ \frac{32}{8}=4 \\ \frac{128}{32}=4 \end{gathered}[/tex]Since each term in the sequence 0.5, 2, 8, 32, 128 except the first term is obtained by multiplying the previous term by a factor 4, the sequence is a geometric sequence.
