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]
Answer: Option a
[tex]\left \{ {{a_1=5} \atop {a_n=a_{(n-1)}+2}} \right.[/tex]
Step-by-step explanation:
The arithmetic sequences have the following explicit formula
[tex]a_n=a_1 +(n-1)*d[/tex]
Where d is the common difference between the consecutive terms and [tex]a_1[/tex] is the first term of the sequence:
The recursive formula for an arithmetic sequence is as follows
[tex]\left \{ {{a_1} \atop {a_n=a_{(n-1)}+d}} \right.[/tex]
Where d is the common difference between the consecutive terms and [tex]a_1[/tex] is the first term of the sequence:
In this case we have the explicit formula [tex]a_n=5+(n-1)*2[/tex]
Notice that in this case
[tex]a_1 = 5\\d = 2[/tex]
Then the recursive formula is:
[tex]\left \{ {{a_1=5} \atop {a_n=a_{(n-1)}+2}} \right.[/tex]
The answer is the option a.
