Let a_1, a_2, a_3, ... be an arithmetic sequence.
If a_{23} = 2/3 and a_{53} = \(5/3\), what is a_{35}?
+9519 Let d be the common difference.
\(\begin{cases}a_{23} = \dfrac23\\a_{53} = \dfrac53\end{cases} \implies \begin{cases}a_1 + 22d = \dfrac23 \\a_1 + 52d = \dfrac53\end{cases}\)
Solving the linear system for a_1 and d gives a_1 = -1/15, d = 1/30.
Therefore, \(a_{35} = a_1 + 34d = -\dfrac1{15} + \dfrac{34}{30} = \dfrac{16}{15}\)
