Find the cardinal number for the set.  = {5, 10, 15, . . . , 45}
A) n() = 9
B) n() = 45
C) The set is infinite.
D) n() = 4

Question

Quizplus · Accepted Answer

The set  = {5, 10, 15, ..., 45} is an arithmetic sequence with a common difference of 5. The sequence starts at 5 and ends at 45. To find the number of terms, use the formula for the nth term of an arithmetic sequence: a_n = a_1 + (n-1)d. Solving for n when a_n = 45, a_1 = 5, and d = 5 gives n = 9.

Find the Cardinal Number for the Set