Question

Given an arithmetic sequence in the table below, create the explicit formula and list any restrictions to the domain. (2 points) n an 1 40 2 47 3 54 an = 40 + 7(n − 1) where n ≥ 40 an = 40 + 7(n − 1) where n ≥ 1 an = 40 − 7(n − 1) where n ≥ 40 an = 40 − 7(n − 1) where n ≥ 1

Answer 1

Answer:

The explicit formula and list any restrictions to the domain is $a_n=40+7(n-1)$ for n≥1

Step-by-step explanation:

Table :

n                            $a_n$

1                             40

2                            47

3                            54

a = first term = 40

d = common difference

So, d = 47-40=54-47 =7

Formula of nth term in A.P. = $a_n=a+(n-1)d$

So, explicit Formula for  for the given sequence = $a_n=40+(n-1)7$

Substitute n = 1 in this explicit formula

$a_1=40+(1-1)7$

$a_1=40$

Put n = 2

$a_1=40+(2-1)7$

$a_1=47$

So, for this explicit formula restrictions to the domain is n≥1

Hence,the explicit formula and list any restrictions to the domain is $a_n=40+7(n-1)$ for n≥1

Answer 2

an = 40 +7(n-1) where n is greater than or equal to 1