Răspuns:
[tex]x \in \varnothing[/tex]
Explicație pas cu pas:
[tex] 1 + 4 + 7 + \cdots + x = 149\\ \\ \text{Progresie aritmetica:}\\ \\ a_1 = 1\\ \\ r = 3\\ \\ a_n = x = 1 + 3(n-1) = 1+3n-3 = 3n-2\\ \\ S_n = \frac{n(3n-2+1)}{2} = 149\\ \\ n(3n-1) = 298\\ \\ 3n^2 - n - 298 = 0\\ \\ \Delta = 1 - 4\cdot 3\cdot (-298) = 1+12\cdot 298 = 1 + 3576 = 3577\\ \implies \sqrt{\Delta}\notin \mathbb{Q} \implies n \notin \mathbb{N} \implies x \in \varnothing[/tex]
