Respuesta :
Answer:
Arithmetic and divergent sequence.
Step-by-step explanation:
We have been given a sequence:
[tex]a_n=4,\frac{10}{3},\frac{8}{3},2...[/tex]
Arithmetic sequence: It is the sequence in which the difference (known as common difference) between consecutive terms is same
Formula for difference: [tex]d=a_n-a_{n-1}[/tex]
Geometric sequence: It is the sequence in which the ratio (known as common ration) between consecutive terms is same.
Formula for ratio: [tex]\frac{a_n}{a_{n-1}}[/tex]
Here, we will first check the common difference
[tex]d=\frac{10}{3}-4=\frac{-2}{3}[/tex]
[tex]\frac{8}{3}-\frac{10}{3}=\frac{-2}{3}[/tex]
[tex]2-\frac{8}{3}=\frac{-2}{3}[/tex]
Hence, we are getting common difference therefore it is an arithmetic sequence.
Arithmetic sequence always diverges
And given sequence being arithmetic will diverge.
Answer:
Arithmetic and divergent sequence.
Step-by-step explanation:
