Question

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.

Answer 1

a)

`\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`

b)

`\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`

Answer 2

tn = 4 + (n -1 )d

t25 = 124

Explanation:

Given

a1 = 5

Equation (General)

an = a1 + (n - 1)*d

Solution

Use any 2 consecutive terms to get d.

t4 =19

t3 = 14

d = t4 - t3

d = 19 - 14

d = 5

tn = 4 + (n - 1)*5

Twenty Fifth Term

t25 = 4 + (25 - 1)*5

t25 = 4 + 24 * 5

t25 = 4 + 120

t25 = 124