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

option D

Explanation:

an arithmetic sequence with a first term of 6 and a second term of 2

First term is 6 and second term is 2. the difference of both the terms is

2- 6= -4

Common difference d= -4

first term a= 6

For explicit equation we use formula

`a_n = a1 + (n-1)d`

Where 'a1' is the first term and d is the common difference

a1= 6, d=-4

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

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

Our first term a1 = 6, so n=1

Hence n represents all integers where n>=1

Answer 2

First term of 6→when n=1→an=a1=6

In the expressions we have a term that contains n-1, then n ≥ 1, then it can be options 1 and 4.

A second term of 2→when n=2→an=a2=2

With the first option when n=2 we get:
a2=6-2(2-1)=6-2(1)=6-2→a2=4 different of 2. This equation doesn't work.

With the fourth option when n=2 we get:
a2=6-4(2-1)=6-4(1)=6-4→a2=2. This equation works.

Answer: Fourth option an = 6 − 4(n − 1); all integers where n ≥ 1