Question
Willow is in her fourth year working for the same company. Her starting salary was
$48,000. The next year, her salary was $50,400. The following year, her salary was
$52,920. This year, her salary is $55,566. Willow’s boss says her salary will continue
to increase by the same percentage each year.
A. Write the values given in the scenario as a sequence. already done.
Year 1: $48,000
Year 2: $50,400
Year 3: $52,920
Year 4: $55,566
$48,000, $50,400, $52,920, $55,566.
B. Is this an example of an arithmetic sequence, a geometric sequence, or
another type of sequence? Explain
make it simple and like a kid wrote it.
$48,000. The next year, her salary was $50,400. The following year, her salary was
$52,920. This year, her salary is $55,566. Willow’s boss says her salary will continue
to increase by the same percentage each year.
A. Write the values given in the scenario as a sequence. already done.
Year 1: $48,000
Year 2: $50,400
Year 3: $52,920
Year 4: $55,566
$48,000, $50,400, $52,920, $55,566.
B. Is this an example of an arithmetic sequence, a geometric sequence, or
another type of sequence? Explain
make it simple and like a kid wrote it.
Answers
GPT-4o mini
B. This is an example of a geometric sequence. In a geometric sequence, each number is multiplied by the same amount to get to the next number.
Let's look at Willow's salaries:
- From Year 1 to Year 2, she went from $48,000 to $50,400. That’s like multiplying by about 1.05 (or 5% increase).
- From Year 2 to Year 3, she went from $50,400 to $52,920. That’s also a little over 5%.
- From Year 3 to Year 4, she went from $52,920 to $55,566, and that's again about a 5% increase.
Since her salary keeps increasing by a percentage (or multiplying by a number), it’s like a pattern where each number gets bigger by the same kind of jump. So we call this a geometric sequence. It’s not just adding the same amount each time, like in an arithmetic sequence.
Let's look at Willow's salaries:
- From Year 1 to Year 2, she went from $48,000 to $50,400. That’s like multiplying by about 1.05 (or 5% increase).
- From Year 2 to Year 3, she went from $50,400 to $52,920. That’s also a little over 5%.
- From Year 3 to Year 4, she went from $52,920 to $55,566, and that's again about a 5% increase.
Since her salary keeps increasing by a percentage (or multiplying by a number), it’s like a pattern where each number gets bigger by the same kind of jump. So we call this a geometric sequence. It’s not just adding the same amount each time, like in an arithmetic sequence.