Question

a sequence is defined by the explicit formula an = 3^n + 4. which recursive formula represents the same sequence of numbers?

Answer 1

`Recursive\ formula\ a_n=3a_(n-1)-8,\ a_1=7`

Explanation:

Recursive Formula: The formula that defines the every term of sequence using previous terms.

`a_n=3^n+4\\\\a_1=3^1+4\\\\a_1=3+4\\\\a_1=7`

`a_n=3^n+4...................................(1)\\\\a_(n-1)=3^(n-1)+4..........................(2)\\\\Multiply\ by\ 3\ both\ the\ sides\\\\3a_(n-1)=3* (3^(n-1)+4)\\\\3a_(n-1)=3* 3^(n-1)+3* 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`

`Recursive\ formula\ a_n=3a_(n-1)-8,\ a_1=7`