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How many integers belong to the arithmetic sequence 13, 20, 27, 34, ..., 2008?

 Jun 1, 2020
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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 \(d = 7, a_n =2008, a_1 = 13 \).

 

\[n = \frac{2008-13}{7} +1= \frac{1995}{7} +1 = 285 +1 = \boxed{286}\]

 Jun 1, 2020

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