Oliver's puppy weighs 6 pounds more each month than it did the month before. If you record the puppy's weight each month, what kind of sequence will you have?

Breakdown the Problem

1. Analyze the weight change of Oliver's puppy over time.
2. Determine the type of sequence based on the weight progression.

Relevant Concepts

1. A sequence can be arithmetic if there is a common difference between consecutive terms.
2. The formula for the n-th term of an arithmetic sequence is given by: $a_n = a_1 + (n-1)d$ where $a_1$ is the first term, $d$ is the common difference, and $n$ is the term number.

Analysis and Detail

1. Let $a_1$ be the initial weight of the puppy at Month 1.
2. According to the problem, every subsequent month the puppy's weight increases by 6 pounds.
3. Therefore, the weight of the puppy after $n$ months can be expressed as: $a_n = a_1 + (n-1)(6)$

Verify and Summarize

• Since there is a constant addition (6 pounds) to the weight every month, this confirms that the sequence of the puppy's weight is indeed arithmetic.

Final Answer

The sequence of the puppy's weight is an arithmetic sequence with a common difference of 6 pounds each month.