Answer:
[tex]a_n=A(n)=3n+3.[/tex]
Step-by-step explanation:
You are given recursive formula [tex]A(n)=A(n-1)+3,[/tex] where [tex]A(1)=6.[/tex]
Find some terms of the sequence:
[tex]a_1=A(1)=6,\\ \\a_2=A(2)=A(1)+3=6+3=9,\\ \\a_3=A(3)=A(2)+3=9+3=12,\\ \\a_4=A(4)=A(3)+3=12+3=15,...[/tex]
You van see that these terms form the arithmetic sequence with first term [tex]a_1=6[/tex] and difference [tex]d=3.[/tex]
An explicit formula for n-th term of arithmetic sequence is
[tex]a_n=a_1+(n-1)d.[/tex]
In your case,
[tex]a_n=6+(n-1)\cdot 3,\\ \\a_n=6+3n-3,\\ \\a_n=3n+3.[/tex]
