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Sweet Time Bakery just opened and is increasing the number of items they bake. For example, the bakery made carrot cakes in December, carrot cakes in January, carrot cakes in February, and carrot cakes in March. What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
Full solution
Q. Sweet Time Bakery just opened and is increasing the number of items they bake. For example, the bakery made carrot cakes in December, carrot cakes in January, carrot cakes in February, and carrot cakes in March. What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
- Identify Sequence Type: To determine the type of sequence, we need to look at the differences or ratios between the terms.
- Calculate Differences: First, let's find the differences between the consecutive terms:January - December: February - January: March - February:
- Confirm Arithmetic Sequence: Since the differences between the consecutive terms are constant, this indicates that the sequence is an arithmetic sequence.
- Check Given Choices: Now, let's check the choices given:(A) arithmetic - This is the correct choice because the differences between the terms are constant.(B) geometric - This would be the case if the ratio between the terms was constant, which it is not.(C) both - A sequence cannot be both arithmetic and geometric unless it is a constant sequence, which this is not.(D) neither - This is not correct because we have already established that the sequence is arithmetic.
