We can use the base formula: [tex]a_n=a_1+(n-1)d[/tex]
[tex]a_n[/tex] = nth term
[tex]a_1[/tex] = first term
[tex]n[/tex] = position of the term
[tex]d[/tex] = common difference
First, lets find the common difference of the sequence.
12 - 5 = 7
19 - 12 = 7
26 - 19 = 7
Second, find the variables we already know.
[tex]a_1[/tex] = 5
[tex]d[/tex] = 7
Put these values into the formula: [tex]a_n = 5+(n-1)7[/tex]
We can use this expression to solve for the fifth term.
[tex]a_5=5+(5-1)7\\a_5=5+(4)(7)\\a_5=5+28\\a_5=33[/tex]
Therefore, the answer is [tex]a_n = 5+(n-1)7[/tex]
Best of Luck!
