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.