Please help me A sequence is defined by the explicit formula a_n=3^n+4. Which recursive formula represents the same sequence of numbers? A. a_n=3a_n_-_1+4;a_1=7 B. a_n=3a_n_-_1-…

Question

Please help me

A sequence is defined by the explicit formula
`a_n=3^n+4`. Which recursive formula represents the same sequence of numbers?

A.
`a_n=3a_n_-_1+4;a_1=7`

B.
`a_n=3a_n_-_1-8;a_1=7`

C.
`a_n=3a_n_-_1-8;a1=7`

D.
`a_n=n^3+6;a_1=7`

Answer 1

Let's write explicitly two consecutive terms:

`a_n = 3^n+4,\qquad a_(n-1) = 3^(n-1) + 4 = (3^n)/(3) + 4`

This means that

`3a_(n-1) = 3^n + 12`

which is 8 more than we expected. So,

`3a_(n-1)-8 = 3^n + 12-8 =3^n + 4 = a_n`

This is options B and C, since their statements seem the same