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A certain arithmetic sequence has the following explicit formula for the nth term: an = 4 + (n - 1)(7) The same sequence has the following recursive formula: an = an-1 + _____ What number belongs in the blank space in the recursive formula?

Respuesta :

an = 4 + (n - 1)(7) 

a1 = 4 + (1-1)*7 = 4
a2 = 4 + (2-1)*7 = 4 + 7

[tex]a_{n} = a_{n-1} +7 [/tex]

7 is common difference of arithmetic sequence.
JeanaShupp

Answer: [tex]a_n=a_{n-1}+7[/tex]

Step-by-step explanation:

We know that the nth term in Arithmetic sequence is given by :-

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

Given: A certain arithmetic sequence has the following explicit formula for the nth term:

[tex]a_n=4+(n-1)(7)[/tex].............................(2)

When we compare (1) and (2), we get

[tex]d=7[/tex]

Also, the recursive formula in A.P. can be written as

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

Therefore, The same sequence has the following recursive formula:

[tex]a_n=a_{n-1}+7[/tex]

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