Question

What are the explicit equation and domain for an arithmetic sequence with a first term of 6 and a second term of 2?

Answer 1

We have to determine the explicit equation and domain for an arithmetic sequence with a first term of 6 and a second term of 2.

Since the first term is 6 and second term is 2. So, the common difference is 2-6 = -4.

So, the arithmetic progression is:

6,2,-2,-6..

So, the nth term of Arithmetic progression is given by:

$a_{n}=a+(n-1)d$

$a_{n}=6+(n-1)(-4)$

$a_{n}=6-4(n-1)$

Since, this sequence involves only sums of integers. So, the domain is integers irrespective of n. But n can only take positive values.

Therefore, the explicit equation is "6 − 4(n − 1)" for all integers where n ≥ 1.