Answer:
[tex]Recursive\ formula\ a_n=3a_{n-1}-8,\ a_1=7[/tex]
Step-by-step explanation:
Recursive Formula: The formula that defines the every term of sequence using previous terms.
[tex]a_n=3^n+4\\\\a_1=3^1+4\\\\a_1=3+4\\\\a_1=7[/tex]
[tex]a_n=3^n+4...................................(1)\\\\a_{n-1}=3^{n-1}+4..........................(2)\\\\Multiply\ by\ 3\ both\ the\ sides\\\\3a_{n-1}=3\times (3^{n-1}+4)\\\\3a_{n-1}=3\times 3^{n-1}+3\times 4\\\\3a_{n-1}=3^{n}+12\\\\3a_{n-1}==3^n+4+8\\\\From\ eq(1)\ 3^n+4=a_n\\\\3a_{n-1}=a_n+8\\\\Subtract\ 8\ from\ the\ both\ sides\\\\3a_{n-1}-8=a_n+8-8\\\\a_n=3a_{n-1}-8[/tex]
[tex]Recursive\ formula\ a_n=3a_{n-1}-8,\ a_1=7[/tex]
