Find the sum of the numbers

sum of the n odd numbres_

1 + 3 + 5 + 7 + . . . . . . .+ n

= n^2 ( n term )

This is an arithmetic sequence with first term $a_1 = 1$ and common difference $d = 2$ . Thus, the general term is given by $a_n = a_1 + (n - 1)d = 2n - 1$ . We can figure out how many terms are in the sequence by solving for $n$ for the last given term:

$a_n = 2n - 1 = 19\quad\Rightarrow\quad n = 10$

And the sum of the first $n$ terms of an arithmetic sequence is given by:

$S_n = \frac{n}{2}(a_1 + a_n)\quad\Rightarrow\quad S_{10} = \frac{10}{2}(1 + 19) = \boxed{100}$