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

Given:

First term of an arithmetic sequence = 5

Second term = 3

To find:

The explicit formula for the given arithmetic sequence.

Solution:

We have,

First term: $a_1=5$

Second term: $a_2=3$

Common difference is

$d=a_2-a_1$

$d=3-5$

$d=-2$

Now, the explicit formula for an arithmetic sequence is

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

where, a is first term and d is common difference.

Putting a=5 and d=-2, we get

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

It can also be written as

$a_n=5-2n+2$

$a_n=7-2n$

Here, n is an integer greater than or equal to 1.

Domain is the set of input values.

Therefore, the explicit equation is $a_n=5+(n-1)(-2)$ or $a_n=7-2n$ and domain is all interest greater than or equal to 1.