A sequence can be defined by the explicit formula a_n=5-3_n . Which recursive formula represents the same sequence of A. a_n=a_n_-_1-3;a_1=5 B. a_n=5-3a_n_-_1;a_1=5 C. a_n=a_n_-…

Question

A sequence can be defined by the explicit formula
`a_n=5-3_n` . Which recursive formula represents the same sequence of

A.
`a_n=a_n_-_1-3;a_1=5`
B.
`a_n=5-3a_n_-_1;a_1=5`
C.
`a_n=a_n_-_1-3;a_1=2`
D.
`a_n=5-3a_n_-_1-3;a_1=2`

Answer 1

Option: C is the correct answer.

C.
`a_n=a_(n-1)-3\ ;\ a_1=2`

Explanation:

The sequence is given by the explicit formula as:

`a_n=5-3n`

where
`a_n` is the nth term of the sequence.

Also, the first term of the sequence is:
`a_1`

i.e.

`a_1=5-3* 1\\\\i.e.\\\\a_1=5-3\\\\i.e.\\\\a_1=2`

Also,

`a_n=5-3n\\\\i.e.\\\\a_n=5-3n+3-3\\\\i.e.\\\\a_n=5-3(n-1)-3\\\\i.e.\\\\a_n=a_(n-1)-3`

Hence, the recursive formula which represents the same sequence is:

Option: C