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At a birthday party, the first child receives smiley stickers, the second child receives smiley stickers, the third child receives smiley stickers, and the fourth child receives smiley stickers. What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
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Q. At a birthday party, the first child receives smiley stickers, the second child receives smiley stickers, the third child receives smiley stickers, and the fourth child receives smiley stickers. What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
- Identify Pattern: Identify the pattern in the sequence of smiley stickers given to each child.Each child receives the same number of smiley stickers, which is . This indicates that the difference between the number of stickers received by any two consecutive children is .
- Check Arithmetic: Determine if the sequence is arithmetic. An arithmetic sequence is one where the difference between consecutive terms is constant. Since each child receives the same number of stickers, the difference between the number of stickers received by any two consecutive children is , which is constant.
- Check Geometric: Determine if the sequence is geometric.A geometric sequence is one where the ratio between consecutive terms is constant. Since each child receives the same number of stickers, the ratio between the number of stickers received by any two consecutive children is (), which is constant.
- Conclude Sequence Type: Conclude the type of sequence based on the definitions.Since the sequence has both a constant difference and a constant ratio, it can be considered both an arithmetic sequence (with a common difference of ) and a geometric sequence (with a common ratio of ).
