If `t_n = 6n + 5`, then `t_(n+1)` =_________.

If T_n = 3n +8 , then T_(n-1) = ________.

If t_n = 3^(n+1) , then S_6 - S_5 = __________.

In a series, if t_n = (n^(2) -1)/(n+1) , then S_6 - S_3= _______.

If t_(n) = 1/((n+1)!) , then sum_(n=1)^(infty) t_(n)=

If t_(n) = 1/((n+1)!) , then sum_(n=1)^(infty) t_(n)=

The fifth term of the sequence for which t_1= 1, t_2 = 2 and t_(n + 2) = t_n + t_(n + 1) is

Prove the following by the method of induction for all n in N : Given t_(n+1) = 5t_(n+4), t_1 = 4. P.T t_n = 5^(n -1)