# Find the first term in the arithmetic sequence __, 8 1/3, 7, 5 2/3, 4 1/3, ...

Find the first term in the arithmetic sequence __, 8 1/3, 7, 5 2/3, 4 1/3, ...
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Alannah Yang
the common difference d of the sequence is
$•xd={a}_{2}-{a}_{1}={a}_{3}-{a}_{2}={a}_{4}-{a}_{3}$
$d=7-8\frac{1}{3}=5\frac{2}{3}-7=-\frac{4}{3}$
$⇒{a}_{1}={a}_{2}-d=8\frac{1}{3}-\left(-\frac{4}{3}\right)=\frac{29}{3}=9\frac{2}{3}$