Question

What is the sum of the first 30 odd numbers? How to calculate it without having to add all of them.

Answer 1

See that odd number are in a Aritmetic progression with a1 = 1 and r = 2

30th number of sequence is given by:

$a_{30}=a_1+29r\\ \\ a_{30}=1+29*2\\ \\ a_{30}=59$

Now you can calculate the sun by:

$S_{30}=\frac{30(1+59)}{2}=\frac{30*60}{2}=900$