Question

find the 5th term of the sequence in which T1=8 and Tn=3t n-1

Answer 1

T_n = 3 * T_(n-1)

Long way (always works!)
T_5 = 3*T_4,
T_4 = 3*T_3
T_3 = 3*T_2
T_2 = 3*T_1

T_5 = 3*3*3*3*T_1 = 81*T_1 = 81*8 = 648!

Short way (sometimes it works!)

T_n = 3^(n-1) * T_1 (this case is a geometric series of ratio-=3)
T_5 = 3^4*8 = 648