Question

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

Answer 1

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 2

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

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,

`a_n = d (n - 1) + c`,

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,

`a_n=-4(n-1)+6`

Or

`a_n=6-4(n-1)`

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.