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8_murik_8 [283]
3 years ago
13

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

divergent.
Mathematics
2 answers:
muminat3 years ago
8 0

Answer:

Arithmetic and divergent sequence.

Step-by-step explanation:

Tresset [83]3 years ago
4 0

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.

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