How many integers belong to the arithmetic sequence 13, 20, 27, 34, ..., 2008?
+43 To find the number of terms in an arithmetic sequence we can use formula
\[n = \frac{a_n - a_1}{d}\].
In this case, n is the number of terms in the sequence so \(a_n\) is the last term of the sequence.
\(d\) is the common difference between each term.
Using this formula we plug in the terms we already know \(d = 7, a_n =2008, a_1 = 13 \).
\[n = \frac{2008-13}{7} +1= \frac{1995}{7} +1 = 285 +1 = \boxed{286}\]
