2. In an arithmetic progression, there are 12 terms, and their sum is 354. The sum of the terms with even indices is to the sum of the terms with odd indices as 32:27. Determine the first term and the common difference of the progression.

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# Solution:

$$
\begin{aligned}
& S_{\text {even }}=\frac{32}{59} \cdot 354=192 ; S_{\text {odd }}=\frac{27}{59} \cdot 354=162 . \\
& \frac{a+d+a+11 d}{2} \cdot 6=192 ; \frac{a+a+10 d}{2} \cdot 6=162 \cdot\left\{\begin{array} { l } 
{ a + 6 d = 3 2 } \\
{ a + 5 d = 2 7 }
\end{array} \Leftrightarrow \left\{\begin{array}{l}
a=2 \\
d=5
\end{array}\right.\right.
\end{aligned}
$$

Answer: $a=2, d=5$.