Question

find the cardinal number for the given set.
a = {8, 12, 16,..., 52}
the cardinal number is
(type a whole number.)

Explanation:

Step1: Identify arithmetic sequence parameters

The set is an arithmetic sequence where first term $a_1=8$, common difference $d=4$, last term $a_n=52$.

Step2: Use arithmetic sequence formula

The nth term formula is $a_n = a_1 + (n-1)d$. Substitute values:
$$52 = 8 + (n-1) \times 4$$

Step3: Solve for n

First subtract 8 from both sides:
$$52 - 8 = (n-1) \times 4$$
$$44 = (n-1) \times 4$$
Divide both sides by 4:
$$\frac{44}{4} = n-1$$
$$11 = n-1$$
Add 1 to both sides:
$$n = 11 + 1 = 12$$

Answer:

12