4)
Termenul general al șirului este :
[tex]\it a_n = S_n - S_{n-1} = \dfrac{n(3n+7)}{2} - \dfrac{(n-1)(3n-3+7)}{2} =
\\\;\\ \\\;\\
\dfrac{3n^2+7n-(n-1)(3n+4)}{2}=\dfrac{3n^2+7n-3n^2-4n+3n+4}{2} =
\\\;\\ \\\;\\
\dfrac{6n+4}{2} = \dfrac{2(3n+2)}{2} = 3n+2\ \ .[/tex]
5d) [tex]\it x_1= 1,\ x_2=4,\ x_{n+1}+x_{n-1} =2(x_n+1) \ \ \ (*)[/tex]
