Question

A puppy weighs 85 lb at birth, and each week he gains 24% in weight. Let an be his weight in pounds at the end of his nth week of life. Is the sequence a1, a2, a3, . . . arithmetic, geometric, or neither? ​

Answer 1

The puppy's weight increases by 24% each week, which means each week's weight is a fixed percentage larger than the previous week's. This pattern of increase is indicative of a geometric sequence, not an arithmetic sequence.

Step-by-step explanation:

The question is asking to determine whether the weekly weight gain of the puppy represents an arithmetic sequence, a geometric sequence, or neither. An arithmetic sequence increases by a fixed amount each time, whereas a geometric sequence increases by a fixed multiplier.

In the case of the puppy, it is given that the puppy weighs 85 lb at birth, and each week it gains 24% of its weight from the previous week. To determine the sequence, let's look at the first few terms:

• Week 0: a0 = 85 lb (birth weight)
• Week 1: a1 = a0 + 0.24 × a0 = 85 + 0.24 × 85 lb
• Week 2: a2 = a1 + 0.24 × a1

From these terms, it is clear that each term is a fixed percentage (24%) larger than the previous term, which is the characteristic of a geometric sequence. Therefore, the sequence representing the puppy's weekly weight is a geometric sequence, not an arithmetic one.