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What are the explicit equation and domain for an arithmetic sequence with a first term of 6 and a second term of 2?
an = 6 − 2(n − 1); all integers where n ≥ 1
an = 6 − 2(n − 1); all integers where n ≥ 0
an = 6 − 4(n − 1); all integers where n ≥ 0
an = 6 − 4(n − 1); all integers where n ≥ 1

Respuesta :

ghanami
hello :
the answer is : 
an = 6 − 4(n − 1); all integers where n ≥ 1
because :
if  n=1    a1 = 6-4(1-1)=6
if n=2     a2 = 6-4(2-1)=2
the common difference is : a2-a1 = 2-6=-4

Answer:

[tex]a_n[/tex] = 6 − 4(n − 1); all integers where n ≥ 1

Step-by-step explanation:

An arithmetic sequence is a sequence in which the difference between each consecutive term is same and this difference is called common difference.

Also, it can be defined by explicit formula,

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

where d is the common difference and c is the first term of the A.P.

Here, first term, c = 6,

And, second term = 2,

So, the common difference, d = Second term - First term = 2 - 6 = -4,

Thus, the explicit formula for the given A.P. is,

[tex]a_n=-4(n-1)+6[/tex]

Or

[tex]a_n=6-4(n-1)[/tex]

Since, the domain of an A.P. is always the set of all natural numbers,

So, Domain of the given A.P. is 1 ≤ n,

Hence, the LAST OPTION  is correct.

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