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A certain arithmetic sequence has the following explicit formula for the nth term: an = 3 + (n – 1)(8) The same sequence has the following recursive formula: an = an – 1 + _____ What number belongs in the blank space in the recursive formula

Respuesta :

CastleRook
From the explicit formula:
a=3
an=3+(n-1)8
an=3+8n-8
an=8n-5
thus:
a2=11, a3=19
Thus the sequence
3,11,19...
thus the recursive formula will be:
an=a(n-1)+8
a1=3
Thus the missing value is: 8

Answer:

Missing number = 8 in the recursive formula

Step-by-step explanation:

The explicit formula for an arithmetic sequence is [tex]a_{n}=a+(n-1)d[/tex]

Here a = first term of the sequence

n = nth term

d = common difference

Explicit formula for an arithmetic sequence is given in the question

[tex]a_{n}=3 + (n -1)8[/tex]

So the first term of the sequence is a = 3

and common difference d = 8

Now the recursive formula of the same sequence will be

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

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

Since d = 8 for the sequence.

[tex]a_{n}=a_{n-1}+8[/tex]

Therefore the missing number is 8 in the recursive formula.

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