Trisha's Pizzeria made 9 pizzas on Monday, 16 pizzas on Tuesday, 25 pizzas on Wednesday, and 36 pizzas on Thursday. What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
Q. Trisha's Pizzeria made 9 pizzas on Monday, 16 pizzas on Tuesday, 25 pizzas on Wednesday, and 36 pizzas on Thursday. What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
Identify Pattern of Pizzas: Let's list the number of pizzas made each day to see if we can identify a pattern:Monday: 9 pizzasTuesday: 16 pizzasWednesday: 25 pizzasThursday: 36 pizzas
Check for Arithmetic Sequence: To determine if this is an arithmetic sequence, we need to check if the difference between consecutive terms is constant.Difference between Tuesday and Monday: 16−9=7Difference between Wednesday and Tuesday: 25−16=9Difference between Thursday and Wednesday: 36−25=11Since the differences are not constant, this is not an arithmetic sequence.
Check for Geometric Sequence: To determine if this is a geometric sequence, we need to check if the ratio between consecutive terms is constant.Ratio of Tuesday to Monday: 916 (not a whole number)Ratio of Wednesday to Tuesday: 1625 (not a whole number)Ratio of Thursday to Wednesday: 2536 (not a whole number)Since the ratios are not constant, this is not a geometric sequence.
Pattern of Perfect Squares: Let's look for another pattern. We notice that the number of pizzas made each day are perfect squares.Monday: 9 (32)Tuesday: 16 (42)Wednesday: 25 (52)Thursday: 36 (62)The sequence of pizzas made each day corresponds to the sequence of perfect squares.
Conclusion: Since the sequence is neither arithmetic nor geometric, and it follows the pattern of perfect squares, the correct choice is:(D) neither
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