Question
At a birthday party, the first child receives 28 smiley stickers, the second child receives 36 smiley stickers, the third child receives 44 smiley stickers, and the fourth child receives 52 smiley stickers. What kind of sequence is this?
Answers
GPT-4o mini
To determine the kind of sequence, we can look at the distribution of smiley stickers received by each child: 28, 36, 44, and 52.
Let's find the differences between each consecutive term:
- The difference between the second child (36) and the first child (28) is:
\[
36 - 28 = 8
\]
- The difference between the third child (44) and the second child (36) is:
\[
44 - 36 = 8
\]
- The difference between the fourth child (52) and the third child (44) is:
\[
52 - 44 = 8
\]
Since the differences between each consecutive pair of terms are all equal to 8, this indicates that the sequence is an **arithmetic sequence**. In an arithmetic sequence, the difference between successive terms is constant. Here, the common difference is 8.
Let's find the differences between each consecutive term:
- The difference between the second child (36) and the first child (28) is:
\[
36 - 28 = 8
\]
- The difference between the third child (44) and the second child (36) is:
\[
44 - 36 = 8
\]
- The difference between the fourth child (52) and the third child (44) is:
\[
52 - 44 = 8
\]
Since the differences between each consecutive pair of terms are all equal to 8, this indicates that the sequence is an **arithmetic sequence**. In an arithmetic sequence, the difference between successive terms is constant. Here, the common difference is 8.