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What is the recursive rule for the sequence? −22.7, −18.4, −14.1, −9.8, −5.5, ... an=an+1+4.3 , where a1=−22.7 an=an−1+4.3 , where a1=−22.7 an=an−1−4.3 , where a1=−22.7 an=an+1−4.3 , where a1=−22.7?

Respuesta :

This is an arithmetic sequence with common difference 4.3

The rule is  an = an-1 + 4.3 where a1 = -22.7

Answer:

The correct option is 2.

Step-by-step explanation:

The given sequence is

−22.7, −18.4, −14.1, −9.8, −5.5, ...

Here first term is -22.7. It means

[tex]a_1=-22.7[/tex]

The common difference is

[tex]d=a_2-a_1=-18.4-(-22.7)=-18.4+22.7=4.3[/tex]

Since we know that

[tex]d=a_n-a_{n-1}[/tex]

[tex]a_n=a_{n-1}+d[/tex]

[tex]a_n=a_{n-1}+4.3[/tex]

Therefore option 2 is correct.

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