Q:

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.

Accepted Solution

A:
Answer:[tex]a_n = 25+3(n-1)[/tex]  [tex]a_{12}=58[/tex]Step-by-step explanation:Given the functions:[tex]f(n) = 25[/tex] and [tex]g(n) = 3(n-1)[/tex]Now, combine them to create an arithmetic sequence i,.e, [tex]a_n[/tex]⇒[tex]a_n = f(n)+g(n)[/tex]then;[tex]a_n = 25+3(n-1)[/tex]            ....[1]We have to find the 12th term;Substitute n = 12 in [1] we have;[tex]a_{12} = 25+3(12-1)[/tex]⇒[tex]a_{12} = 25+3(11)[/tex]⇒[tex]a_{12} = 25+33 = 58[/tex]Therefore, the 12th term is 58