Решите уравнение: 2+5+8+…+x=126, где x – натуральное число.

\[2 + 5 + 8 + .. + x = 126\]

\[d = 5 - 2 = 3;\ \ \]

\[a_{n} = 2 + 3 \cdot (n - 1) = x\]

\[x = 3n - 1\]

\[S = \frac{2 + 3n - 1}{2} \cdot n = 126\]

\[(3n + 1) \cdot n = 252\]

\[3n^{2} + n - 252 = 0\]

\[D = 1 + 3024 = 3025\]

\[n_{1} = \frac{- 1 - 55}{6} < 0\]

\[n_{2} = \frac{- 1 + 55}{6} = 9\]

\[x = 27 - 1 = 26.\]

\[Ответ:x = 26.\]