Question

1. - / 6.25 points 0/100 submissions used

find the cardinality of the following set.
{3, 6, 9, 12, 15, ... , 384}

Explanation:

Step1: Identify sequence type

This is an arithmetic sequence where each term is 3 times a positive integer, so the set can be rewritten as $\{3n \mid n \in \mathbb{N}, 3n \leq 384\}$.

Step2: Solve for n

Divide the last term by 3 to find the maximum n:
$\frac{384}{3} = 128$

Step3: Count elements

The values of n are 1,2,...,128, so there are 128 elements.

Answer:

128