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Let a1, a2, a3, ..., a10 be an arithmetic series.  If a1 + a3 = -2 and a2 + a4 + a6 = 1, then find a1.

 May 13, 2024
 #1
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Suppose \(d = a_2 - a_1\). Note that the given conditions are equivalent to:

\(\begin{cases} a_1 + d = -1\\ a_1 + 3d = \dfrac13 \end{cases}\)

 

Solving gives \(d = \dfrac23\) and \(a_1 = -\dfrac53\).

 May 13, 2024

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