Solve {l}{text{oranA.P.}mT_{m}=nT_{n}text{,prove}T_{m+n}=0}{a+(m-1)d]=n[a+(n-1)d]}

$$\left. \begin{array} { l } { \text { or an A.P. } m T _ { m } = n T _ { n } \text { , prove } T _ { m + n } = 0 } \\ { a + ( m - 1 ) d ] = n [ a + ( n - 1 ) d ] } \end{array} \right.$$

Solve for m, T_m, n, T_n

$$m=\frac{T_{n}n}{T_{m}}\text{, }T_{m}\neq 0\text{, }n\in \mathrm{R}\text{, }T_{n}\in \mathrm{R}$$

$$m\in \mathrm{R}\text{, }T_{m}=0\text{, }n=0\text{, }T_{n}\in \mathrm{R}$$

$$m\in \mathrm{R}\text{, }T_{m}=0\text{, }n\in \mathrm{R}\text{, }T_{n}=0$$