Pls help, question: “ write an equation in the form y=mx+b that represents this table.”

Given:

The different recursive formulae.

To find:

The explicit formulae for the given recursive formulae.

Solution:

The recursive formula of an arithmetic sequence is and the explicit formula is , where a is the first term and d is the common difference.

The recursive formula of a geometric sequence is and the explicit formula is , where a is the first term and r is the common ratio.

The first recursive formula is:

for .

It is the recursive formula of an arithmetic sequence with first term 5 and common difference 5. So, the explicit formula for this recursive formula is:

Therefore, the correct option is A, i.e., .

The second recursive formula is:

for .

It is the recursive formula of a geometric sequence with first term 5 and common ratio 3. So, the explicit formula for this recursive formula is:

Therefore, the correct option is F, i.e., .

The third recursive formula is:

for .

It is the recursive formula of an arithmetic sequence with first term 5 and common difference 3. So, the explicit formula for this recursive formula is:

Therefore, the correct option is D, i.e., .