Question

The cardinal number of {208,209,210,211,....,1007} is

Answer 1

Answer:

$\large \boxed{800}$

Step-by-step explanation:

A cardinal number is the number of distinct elements in a finite set.

Your set consists the integers from 208 to 1007.

Each element is 1 more than the preceding element, so it represents an arithmetic sequence with distinct elements.

The formula for  the nth term in an arithmetic sequence is

aₙ = a₁ + (n - 1)d, where

a₁ = the first element of the sequence

n = the common difference between successive terms

In your sequence,

a₁ = 208 and d = 1

To figure out how many elements are in the set, set aₙ to 1007 —  the last member —  and solve for n.

$\begin{array}{rcl}a_{n} & = & a_{1} + (n - 1)d\\1007 & = & 208 + (n - 1) \times 1\\1007 & = &208 + n - 1\\1007 & = &207 + n\\n & = & \mathbf{800}\\\end{array}\\\text{The cardinal number is \large \boxed{\mathbf{800}} }$