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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

User Ben Last
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1 Answer

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A sequence is "arithmetic", if the difference between 2 consecutive terms is always equal.

That is, a sequence
(a_n) is arithmetic if:


a_2-a_1=a_3-a_2=a_4-a_3=.....d, 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
a_2-a_1=2-6=-4,

so we construct the sequence as follows:


a_1=6


a_2=6+(-4)=2


a_3=[6+(-4)]+(-4)=-2


a_4=[6+(-4)+(-4)]+(-4)=-6


a_5=[6+(-4)+(-4)+(-4)]+(-4)=-10

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thus clearly
a_n=[6+(-4)(n-1)=a_n=[6-4(n-1)

and n∈{1, 2, 3, 4...}


Answer:

an = 6 − 4(n − 1); all integers where n ≥ 1

User Dane Lee
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