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

an = 13 + (n - 1)(6)

The same sequence has this recursive formula:

an = an - 1 + _____

What number belongs in the blank space in the recursive formula?

Respuesta :

The number 6 could replace the gap :)

Answer:

Answer is 6

Step-by-step explanation:

Given that there is an arithmetic sequence and has an explicit formula for the nth term as

[tex]a_n =13+(n-1)6\\[/tex]

Since n can be any natural number, let us substitute n =1 to find the I term

[tex]a_1 = 13+(1-1)6=13[/tex]

Let us find the 2nd term by substituting n=2

[tex]a_2 =13+(2-1)6=19[/tex]

Common difference = d= [tex]a_2-a_1=19-13=6[/tex]

Hence from I term a and common difference d, we find the any term can be obtained by adding 6 to the previous term

i.e. [tex]a_n=a_{(n-1) +6}[/tex]

6 is the answer

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