Question

A sequence can be defined by the explicit formula _n" alt="a_n=5-3_n" align="absmiddle" class="latex-formula"> . 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

Answer:

Option: C is the correct answer.

            C.  $a_n=a_{n-1}-3\ ;\ a_1=2$

Step-by-step 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.

$a_1=5-3\times 1\\\\i.e.\\\\a_1=5-3\\\\i.e.\\\\a_1=2$

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