Write the following sets in roaster form :- 1. A = {An: n€N , An+1 =

1.	Write the following sets in roaster form :- 1. A = {An: n€N , An+1 = 3An and A1= 2 }
Answer» $Given \: A=\{A_{n}:n\in N , A_{n+1} = 3A_{n} \:and \: A_{1} = 2 \}$ $i )A_{1} = 2 \: --(1)$ $ii ) If \: n = 1 \implies A_{1+1} = 3 \times A_{1}$ $\implies A_{2} = 3 \times 2 = 6$ $iii ) If \: n = 2 \implies A_{2+1} = 3 \times A_{2}$ $\implies A_{3} = 3 \times 6 = 18$ $iv ) If \: n = 3 \implies A_{3+1} = 3 \times A_{3}$ $\implies A_{4} = 3 \times 18 = 54$ $v ) If \: n = 4 \implies A_{4+1} = 3 \times A_{4}$ $\implies A_{5} = 3 \times 54 = 162$ THEREFORE., $\red{ Roster \: form \: of \: set \: A }$ $\green { = \{ 2,6,18,162, \ldots \}}$ •••♪