A sequence is "arithmetic", if the difference between 2 consecutive terms is always equal.
That is, a sequence [tex](a_n)[/tex] is arithmetic if:
[tex]a_2-a_1=a_3-a_2=a_4-a_3=.....d[/tex], where d is called the "common difference".
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Consider the sequence with a first term of 6 and a second term of 2
the common difference d is [tex]a_2-a_1=2-6=-4[/tex],
so we construct the sequence as follows:
[tex]a_1=6[/tex]
[tex]a_2=6+(-4)=2[/tex]
[tex]a_3=[6+(-4)]+(-4)=-2[/tex]
[tex]a_4=[6+(-4)+(-4)]+(-4)=-6[/tex]
[tex]a_5=[6+(-4)+(-4)+(-4)]+(-4)=-10[/tex]
.
.
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thus clearly [tex]a_n=[6+(-4)(n-1)=a_n=[6-4(n-1)[/tex]
and n∈{1, 2, 3, 4...}
Answer:
an = 6 − 4(n − 1); all integers where n ≥ 1
