Question

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 ​

Answer 1

Answer:

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,…}

Answer 2

Answer:

hope this answer help you