which of the following recursive formulas represent the same arithmetic sequence as the explicit formula an=5+(n-1)2a. a1=5an=an-1+2b. a1=5an=(an-1+2)5c. a1=2an=an-1+5d. a1=2an=an-1*5

Answer:Choice A:[tex]a_1=5[/tex][tex]a_{n}=a_{n-1}+2[/tex]Step-by-step explanation:[tex]a_n=5+(n-1)2[/tex]means we looking for first term 5 and the sequence is going up by 2.In general,[tex]a_n=a_1+(n-1)d[/tex]means you have first term [tex]a_1[/tex] and the sequence has a common difference of d.So it is between the first two choices.The explicit form of an arithmetic sequence is: [tex]a_n=a_1+(n-1)d[/tex]An equivalent recursive form is [tex]a_n=a_{n-1}+d \text{ where } a_1 \text{ is the first term}[/tex]So d again here is 2.So choice a is correct.[tex]a_1=5[/tex][tex]a_{n}=a_{n-1}+2[/tex]