Question
Hazel spends $30 on groceries each week. If you write down a list of her total spending over time, what kind of sequence will you have?
Answers
GPT-4o mini
If Hazel spends $30 on groceries each week, her total spending forms an arithmetic sequence.
In an arithmetic sequence, each term after the first is found by adding a constant difference to the previous term. Here, the first term (spending in the first week) is $30, and the common difference is also $30 (the amount spent each subsequent week).
The total spending after \( n \) weeks can be represented as:
- Week 1: \( 30 \times 1 = 30 \)
- Week 2: \( 30 \times 2 = 60 \)
- Week 3: \( 30 \times 3 = 90 \)
- Week 4: \( 30 \times 4 = 120 \)
- And so on...
The \( n \)-th term of this sequence can be expressed as:
\[ a_n = 30n \]
Thus, the sequence of Hazel's total spending over time is 30, 60, 90, 120, ..., which is an arithmetic sequence with a common difference of $30.
In an arithmetic sequence, each term after the first is found by adding a constant difference to the previous term. Here, the first term (spending in the first week) is $30, and the common difference is also $30 (the amount spent each subsequent week).
The total spending after \( n \) weeks can be represented as:
- Week 1: \( 30 \times 1 = 30 \)
- Week 2: \( 30 \times 2 = 60 \)
- Week 3: \( 30 \times 3 = 90 \)
- Week 4: \( 30 \times 4 = 120 \)
- And so on...
The \( n \)-th term of this sequence can be expressed as:
\[ a_n = 30n \]
Thus, the sequence of Hazel's total spending over time is 30, 60, 90, 120, ..., which is an arithmetic sequence with a common difference of $30.