Question

What are the explicit equation and domain for an arithmetic sequence with a first term of 7 and a second term of 3?

A. an = 7 − 4(n − 1); all integers where n ≥ 1
B. an = 7 − 4(n − 1); all integers where n ≥ 0
C. an = 7 − 3(n − 1); all integers where n ≥ 1
D. an = 5 − 3(n − 1); all integers where n ≥ 0

Answer 1

A

Explanation:

A is the correct answer

Answer 2

I am detailing it to show you how to calculate an explicite equation

Arithmetic Progression First term 7 , second 3 hence d=3-7 = - 4


n=Term rank ==>║ 1 2 3 4 5 6 7......n
Value ====>║ 7 3 -1 -5 -9 -13 -17.......

a(n) (sub Notation║ a₁ a₂ a₃ a₄ a₅ a₆ a₇.....a(n)


Term 1 = a₁ = 7........................7-4(0)
Term 2 = a₂ = 3........................7-4(1)
Term 3 = a₃ = -1.......................7-4(2)
Term 4 = a₄ = -5.......................7-4(3)
Term 5 = a₅ = -9.......................7-4(4)
Term n = a(n) ============7-4(n-1)
So A. an = 7 − 4(n − 1); all integers where n ≥ 1