$\text{Câu 1: }\\u_n=n+1\\\text{Ta có: } u_{n+1}=n+1+1=n+2\\\text{Xét hiệu }u_{n+1}-u_n=n+2-n-1=1>0\\\to u_{n+1}>u_n\\\to \text{Dãy số là dãy số tăng }\\\text{Câu 2: }\\\begin{cases}u_1+u_5=7\\u_3+u_4=9\end{cases}\to \begin{cases} u_1+u_1+4d=7\\u_1+2d+u_1+3d=9\end{cases}\\\to \begin{cases} 2u_1+4d=7\\2u_1+5d=9\end{cases}\to \begin{cases} u_1=-\dfrac{1}{2}\\d=2\end{cases}\\\to u_1=-\dfrac{1}{2};\,u_2=\dfrac{3}{2};\,u_3=\dfrac{7}{2};\,u_4=\dfrac{11}{2};\,u_5=\dfrac{15}{2}\\\text{Câu 3: }\\\begin{cases}u_4=25\\u_3=5\end{cases}\to \begin{cases}u_1q^3=25\\u_1q^2=5\end{cases}\\\to \begin{cases}u_1=\dfrac{25}{q^3}\\\dfrac{25}{q^3}.q^2=5\end{cases}\to \begin{cases} u_1=\dfrac{25}{q^3}\\q=5\end{cases}\\\to \begin{cases}u_1=\dfrac{1}{5}\\q=5\end{cases}\\\to u_1=\dfrac{1}{5};\,u_2=1;\,u_3=5;\,u_4=25;\,u_5=125$
