Question

Classify the sequence {a_n}={4,10/3,8/3,2...} as arithmetic or geometric. Then, determine whether the sequence is convergent or divergent.

Answer 1

Answer:

Arithmetic and divergent sequence.

Step-by-step explanation:

Answer 2

Answer:

Arithmetic and divergent sequence.

Step-by-step explanation:

We have been given a sequence:

$a_n=4,\frac{10}{3},\frac{8}{3},2...$

Arithmetic sequence: It is the sequence in which the difference (known as common difference) between consecutive terms is same

Formula for difference: $d=a_n-a_{n-1}$

Geometric sequence: It is the sequence in which the ratio (known as common ration) between consecutive terms is same.

Formula for ratio: $\frac{a_n}{a_{n-1}}$

Here, we will first check the common difference

$d=\frac{10}{3}-4=\frac{-2}{3}$

$\frac{8}{3}-\frac{10}{3}=\frac{-2}{3}$

$2-\frac{8}{3}=\frac{-2}{3}$

Hence, we are getting common difference therefore it is an arithmetic sequence.  

Arithmetic sequence always diverges

And given sequence being arithmetic will diverge.