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

Choice A:

Step-by-step explanation:

means we looking for first term 5 and the sequence is going up by 2.

In general,

means you have first term 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:

An equivalent recursive form is

So d again here is 2.

So choice a is correct.

Option a

Step-by-step explanation:

The arithmetic sequences have the following explicit formula

Where d is the common difference between the consecutive terms and is the first term of the sequence:

The recursive formula for an arithmetic sequence is as follows

Where d is the common difference between the consecutive terms and is the first term of the sequence:

In this case we have the explicit formula

Notice that in this case

Then the recursive formula is:

The answer is the option a.

the answer is a

step-by-step explanation: