Question

A sequence can be defined by the explicit formula an=5-3n Which recursive formula represents the same sequence of numbers?

Answer 1

Answer:

$a_{n+1}=a_n-3$

or

$f(n+1)=f(n)-3.$

Step-by-step explanation:

Consider the sequence formed using rule $a_n=5-3n:$

• when $n=0,$ $a_0=5-3\cdot 0=5;$
• when $n=1,$ $a_1=5-3\cdot 1=2;$
• when $n=2,$ $a_2=5-3\cdot 2=-1\ ...$

You can see that each next term of the sequence is less than previous by 3. Thus, the recursive formula that represents the same sequence of numbers is

$a_{n+1}=a_n-3$

or

$f(n+1)=f(n)-3.$

Answer 2

Answer:

an= an - 1 - 3; a1 = 2