Question

(Worth 30 points) What are the explicit equation and domain for an arithmetic sequence with a first term of 5 and a second term of 3? (Answers are attached as a picture)

Answer 1

Answer:

$a_n=5-2(n-1)$, all integers where n≥1

Step-by-step explanation:

we know that

The explicit equation for an arithmetic sequence is equal to

$a_n=a_1+d(n-1)$

a_n is the th term

a_1 is the first term

d is the common difference

n is the number of terms

we have

$a_1=5\\a_2=3$

Remember that

In an Arithmetic Sequence the difference between one term and the next is a constant, and this constant is called the common difference.

To find out the common difference subtract the first term from the second term

$d=a_2-a_1=3-5=-2$

substitute the given values in the formula

$a_n=5-2(n-1)$

The domain is all integers for $n\geq 1$