Question

Write the following sets in roaster form :-
1. A = {An: n€N , An+1 = 3An and A1= 2 }

Answer 1

$Given \: A=\{A_{n}:n\in N , A_{n+1} = 3A_{n} \:and \: A_{1} = 2 \}$

$i )A_{1} = 2 \: --(1)$

$ii ) If \: n = 1 \implies A_{1+1} = 3 \times A_{1}$

$\implies A_{2} = 3 \times 2 = 6$

$iii ) If \: n = 2 \implies A_{2+1} = 3 \times A_{2}$

$\implies A_{3} = 3 \times 6 = 18$

$iv ) If \: n = 3 \implies A_{3+1} = 3 \times A_{3}$

$\implies A_{4} = 3 \times 18 = 54$

$v ) If \: n = 4 \implies A_{4+1} = 3 \times A_{4}$

$\implies A_{5} = 3 \times 54 = 162$

Therefore.,

$\red{ Roster \: form \: of \: set \: A }$

$\green { = \{ 2,6,18,162, \ldots \}}$

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Answer 2

Answer:

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