EXAMPLE 11 Write the following sets in Roster form:
(1) A = lanine N, an+ 1 3an, and a
(ii) B = lanine N, 2n+2 = an+1+an, a = ay = 1)
a = 21there is no victory without a battle there is no victory without a battle
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GivenA={A
n
:n∈N,A
n+1
=3A
n
andA
1
=2}
i )A_{1} = 2 \: --(1)i)A
1
=2−−(1)
ii ) If \: n = 1 \implies A_{1+1} = 3 \times A_{1}ii)Ifn=1⟹A
1+1
=3×A
1
\implies A_{2} = 3 \times 2 = 6⟹A
2
=3×2=6
iii ) If \: n = 2 \implies A_{2+1} = 3 \times A_{2}iii)Ifn=2⟹A
2+1
=3×A
2
\implies A_{3} = 3 \times 6 = 18⟹A
3
=3×6=18
iv ) If \: n = 3 \implies A_{3+1} = 3 \times A_{3}iv)Ifn=3⟹A
3+1
=3×A
3
\implies A_{4} = 3 \times 18 = 54⟹A
4
=3×18=54
v ) If \: n = 4 \implies A_{4+1} = 3 \times A_{4}v)Ifn=4⟹A
4+1
=3×A
4
\implies A_{5} = 3 \times 54 = 162⟹A
5
=3×54=162
Therefore.,
\red{ Roster \: form \: of \: set \: A }RosterformofsetA
\green { = \{ 2,6,18,162, \ldots \}}={2,6,18,162,…}
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