Question

What are the explicit equation and domain for an arithmetic sequence with a first term of 5 and a second term of 2?

Answer 1

`a_n= 8-3n` is the explicit equation, integers n>0

Explanation:

an arithmetic sequence with a first term of 5 and a second term of 2

General formula for arithmetic sequence is
`a_n= a_1+(n-1)d`

where a1 is the first term and d is the common difference

`a_1=5`

`a_2=2`

Difference between the terms = 2-5=-3

Difference d=-3

a1=5, d=-3, plug in all the values

`a_n= 5+(n-1)(-3)`

multiply -3 inside the parenthesis

`a_n= 5-3n+3`, combine like terms

`a_n= 8-3n` is the explicit equation, n>0

Answer 2

For the answer to the question above asking the explicit equation and domain for an arithmetic sequence with the first term of 5 and the second term of 2? I think the answer for this is 5-2(n-1); all integers where n≥0. I hope this helps.