Question

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

Answer 1

Answer:

A

Step-by-step explanation:

In Arithmetic sequence , 2nd term = first term + d

3rd term = 2nd term + d

In this given explicit formula, we  can find that d =2

an ----> n th term;   an-1 -----> n-1 th term

an = an-1 th term + 2

Answer 2

Answer:

A.

Step-by-step explanation:

The given expression is

$a_{n}=5+(n-1)2$

To right well a recursive formula for arithmetic sequences, we first need to write down the first term of the sequence. So, the recursive formula must have $a_{1}=5$ in first place. That gives A and B as possible answers.

Then, we have to write the pattern rule to get all terms that goes after the first one. So, if you look closely, choice A is the one that is using a pattern to built the arithmetic sequence. On the other hand, choice B doesn't make sense due to its factor 5, that will not give the same arithmetic sequence.

Therefore, the right answer is A.