Question

Emanuel is writing a novel. he writes 10 pages on the first day. every day after that, emanuel writes 16 more pages. let y represent the total number of pages emanuel writes after x days. which type of sequence does this situation represent?

a. the situation represents a geometric sequence because the successive y-values have a common ratio of 6.
b. the situation represents an arithmetic sequence because the successive y-values have a common difference of 6.
c. the situation represents a geometric sequence because the successive y-values have a common ratio of 16.
d. the situation represents an arithmetic sequence because the successive y-values have a common difference of 16.

Answer 1

arithmetic, difference of 16

Explanation:

The situation represents an arithmetic sequence. In fact, two consecutive terms of an arithmetic sequence differ by a fixed quantity - the common difference.

On the other hand, in a geometric sequence, two consecutive terms are in the same ratio - the common ratio.

In this case, Emanuel writes 16 pages more with each passing day, so if you compare two consecutive days, the number of pages differ by 16, it's not 16 times as much.

So, the sequence is arithmetic, and the common DIFFERENCE is 16.

Answer 2

The situation represents an arithmetic sequence. In fact, two consecutive terms of an arithmetic sequence differ by a fixed quantity - the common difference.

On the other hand, in a geometric sequence, two consecutive terms are in the same ratio - the common ratio.

In this case, Emanuel writes 16 pages more with each passing day, so if you compare two consecutive days, the number of pages differ by 16, it's not 16 times as much.

So, the sequence is arithmetic, and the common ratio is 16.