Answer
$900$
Work Step by Step
We have to determine the sum:
$S=1+3+5+.....+59$
As $3-1=5-3=...=2$, the sequence is arithmetic.
Determine its first term and the common difference:
$a_1=1$
$d=2$
The terms can be written as:
$1=2\cdot 1-1$
$3=2\cdot 2-1$
$5=2\cdot 3-1$
..............................
$59=2\cdot 30-1$
Therefore, the given sum contains $30$ terms, so we have to determine the sum of the first $30$ terms. We use the formula:
$S_n=\dfrac{n(a_1+a_n)}{2}$
$1+3+5+...+59=\dfrac{30(1+59)}{2}$
$=\dfrac{30\cdot 60}{2}$
$=900$
