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# help

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

Jun 1, 2020

#1
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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