contestada

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.

Respuesta :

[tex]\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}\\\\ -------------------------------\\\\[/tex]

[tex]\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[/tex]

and fairly sure you know how much that is.
JeanaShupp

Answer with explanation:

Given functions : [tex]f(n)=25[/tex] and [tex]g(n)=3(n-1)[/tex]

When we combine then to  create an arithmetic sequence [tex]A_n[/tex], we get

[tex]A_n=f(n)+g(n)\\\\\Rightarrow\ A_n=25+3(n-1)[/tex]

To solve for 12th term , we put n= 12 in [tex]A_n[/tex], we get

[tex]A_{12}=25+3(12-1)\\=25+3(11)\\=25+33=58[/tex]

Hence, the value of 12th term of [tex]A_n[/tex] = 58

Otras preguntas