Mathematics, 04.07.2019 06:00 Rogeartest4
Use the sequence 4, 9, 14, 19, a. find a function to model the sequence, assuming 4 is the first term. show your work. b. use your model to find the 25th term of the sequence.
Answers: 2
![\bf 4~~,~~\stackrel{4+5}{9}~~,~~\stackrel{9+5}{14}~~,~~\stackrel{14+5}{19}~~...\impliedby ~\hspace{5em}\stackrel{\textit{common difference}}{+5} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 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}\\[-0.5em] \hrulefill\\ a_1=4\\ d=5 \end{cases} \\\\\\ a_n=4+(n-1)5](/tpl/images/0049/1957/5844e.png)
![\bf \stackrel{\textit{25th term}}{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}\\[-0.5em] \hrulefill\\ a_1=4\\ d=5\\ n=25 \end{cases} \\\\\\ a_{25}=4+(25-1)5\implies a_{25}=4+(24)5 \\\\\\ a_{25}=4+120\implies a_{25}=124](/tpl/images/0049/1957/e94de.png)
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Use the sequence 4, 9, 14, 19, a. find a function to model the sequence, assuming 4 is the first te...
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