Respuesta :

carlosego

Answer: first option.

Step-by-step explanation:

Find the common difference d of the arithmetic sequence:

[tex]d=a_n-a_{(n-1)}\\d=989-997\\d=-8[/tex]

Then the formula for the 101st term is the shown below:

[tex]a_n=a_1+(n-1)d[/tex]

Where:

[tex]a_1=997\\d=-8\\n=101[/tex]

Substitute values into the formula. Therefore, you obtain:

[tex]a_n=997+(101-1)(-8)=197[/tex]

kudzordzifrancis

Answer:

[tex]a_{101}=197[/tex]

Step-by-step explanation:

The first term of the sequence is

[tex]a_1=997[/tex]

The given sequence  is 997, 989, 981, ...

The common difference is

[tex]d=989-997=-8[/tex]

The nth ter of the sequence is

[tex]a_n=a_1+d(n-1)[/tex]

We plug in the first term and the common ratio to obtain;

[tex]a_n=997-8(n-1)[/tex]

[tex]a_n=997-8n+8[/tex]

[tex]a_n=1005-8n[/tex]

We substitute n=101 to get;

[tex]a_{101}=1005-8(101)[/tex]

[tex]a_{101}=197[/tex]

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