Question

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

Answer 1

A.

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.

Answer 2

A

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