Respuesta :
We need to identify the type of the sequence and the common difference for arithmetic sequences and common ratio for geometric sequences.
For sequence 1:
[tex]\begin{gathered} \text{Sequence: -5, 0, 5, 10} \\ a_n=a_{n-1}+5 \\ a_n-a_{n-1}=5 \end{gathered}[/tex]The sequence is arithmetic and the common difference is 5.
For sequence 2:
[tex]\begin{gathered} \text{Sequence: 8, 4, 2, 1} \\ a_n=\frac{a_{n-1}}{2} \\ \frac{a_n}{a_{n-1}}=\frac{1}{2} \end{gathered}[/tex]The sequence is geometric and the common ratio is 1/2.
For sequence 3:
[tex]\begin{gathered} \text{Sequence: }8,\text{ 16/3, 32/9, 64/27} \\ a_n=a_{n-1}\cdot\frac{2}{3} \\ \frac{a_n}{a_{n-1}}=\frac{2}{3} \end{gathered}[/tex]The sequence is geometric and the common ratio is 2/3.
For sequence 4:
[tex]\begin{gathered} \text{Sequence: 27, 23, 19, 15} \\ a_n=a_{n-1}-4 \\ a_n-a_{n-1}=-4 \end{gathered}[/tex]The sequence is arithmetic and the common difference is -4.
