Question

What are the explicit equation and domain for an arithmetic sequence with a first term of 5 and a second term of 3?

Answer 1

In mathematics, number sequences are classified into three types: arithmetic progression, geometric progression and harmonic progression. Arithmetic sequences have a common difference, geometric sequences have a common ration, while harmonic progression is just the reciprocal of the arithmetic progression.

The first term of the arithmetic sequence is 5, followed by three. Therefore, the common difference is, 3-5 = -2. You use these values to the derived formulas for arithmetic progression. One of these formulas is

An = A1 + (n-1)d
where
An is the nth term in the sequence
A1 is the first term of the sequence
n is the totla number of terms within the sequence
d is the common difference.

In this problem, A1 = 5 and d=2. Substituting to the equation,

An = 5 + (-2)(n-1)
An = 5 - 2(n-1), where n should be more than 1. In order for it to become a sequence, it should contain more than one term.

So, the answer is letter D.