MATH SOLVE

3 months ago

Q:
# Which of the following recursive formulas represents the same arithmetic sequence as the explicit formula an=5+(n-1)2?

Accepted Solution

A:

Answer:[tex]a_1 = 5[/tex][tex]a_n = a_{n-1} + 2[/tex]Step-by-step explanation:Given[tex]a_n = 5 + (n - 1)2[/tex]RequiredThe equivalent recursive functionThe general explicit function is:[tex]a_n = a_1+ (n - 1)d[/tex]So, by comparison[tex]a_1 = 5[/tex][tex]d = 2[/tex]The recursion of an arithmetic sequence is:[tex]a_n = a_{n-1} + d[/tex]Substitute 2 for d[tex]a_n = a_{n-1} + 2[/tex]Hence: (a) is correct