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

`\bf n^(th)\textit{ term of an arithmetic sequence}\\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^(th)\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference} \end{cases}\\\\ -------------------------------\\\\`


`\bf \begin{cases} f(n)=25\\ g(n)=3(n-1) \end{cases}\qquad \begin{array}{llll} f(n)+g(n)\implies &25+(n-1)&3\\ &\uparrow &\uparrow \\ &a_1&d \end{array}\\\\ -------------------------------\\\\ 12^(th)\textit{ term of an arithmetic sequence}\\\\ a_(12)=a_1+(12-1)d\qquad \begin{cases} n=n^(th)\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\ ----------\\ d=3\\ a_1=25\\ n=12 \end{cases} \\\\\\ a_(12)=25 + (12-1)3`

and fairly sure you know how much that is.

Answer 2

Answer with explanation:

Given functions :
`f(n)=25` and
`g(n)=3(n-1)`

When we combine then to create an arithmetic sequence
`A_n`, we get

`A_n=f(n)+g(n)\\\\\Rightarrow\ A_n=25+3(n-1)`

To solve for 12th term , we put n= 12 in
`A_n`, we get

`A_(12)=25+3(12-1)\\=25+3(11)\\=25+33=58`

Hence, the value of 12th term of
`A_n` = 58