We can manipulate the arithmetic sequence formula to solve this problem.
Let's look at [tex]a_{n} = a_{1} +(n-1)d[/tex] where [tex]a_{n}[/tex] is the [tex]n^{th}[/tex] term, [tex]a_{1}[/tex] is the first term, [tex]n[/tex] is the number of terms, and [tex]d[/tex] is the common difference. We already know that [tex]a_{1}[/tex] is equal to [tex]14[/tex], [tex]n[/tex] is equal to [tex]25[/tex], and [tex]a_{25}[/tex] is equal to [tex]206[/tex]. This therefore leave us with only the common difference to solve.
Manipulating the formula we can arrive at the answer:
[tex]206 = 14 +(25-1)d[/tex]
[tex]192 = (24)d[/tex]
[tex]d=8[/tex]
ANSWER: The common difference is 8.
