[tex]a_n=a_1+(n-1)r\\\\\displaystyle S_n=\frac{a_1+a_n}{2}\cdot n\\\\\displaystyle S_{30}=\frac{a_1+a_{30}}{2}\cdot 30=\frac{a_1+a_1+29r}2=\frac{2a_1+29r}2\\\\a_7+a_{14}+a_{16}+a_{25}=80\\a_1+6r+a_1+13r+a_1+15r+a_1+24r=80\\4a_1+58r=80|:2\\2a_1+29r=40\\\\\displaystyle S_{30}=\frac{40}2\cdot30=600[/tex]
