Question

Given the functions f(n) = 25 and g(n) = 3(n − 1), combine them to create an arithmetic sequence, an, and solve for the 12th term.

Answer 1

An arithmetic sequence can be defined using the first term f(n) and the common difference in the g(n) term. In this case, we have:
a(n) = f(n) + g(n) = 25 + 3(n-1) = 3n + 22
If we want to find the 12th term, we substitute n = 12 into a(n):
a(12) = 3(12) + 22 = 36 + 22 = 58

Answer 2

Answer:
`a(n)=22+3n`

The 12th term of a(n) is 58.

Explanation:

Given the functions f(n) = 25 and g(n) = 3(n − 1)

Let the combined function of f(n) and g(n) be a(n).

Then
`a(n)=f(n)+g(n)`

`a(n)=25+3(n-1)=25+3n-3=25-3+3n=22+3n`

Thus,
`a(n)=22+3n`

To find the value of the 12th term of a(n), substitute n=12, we get

`a(12)=22+3(12)=22+36=58`