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)=(30(1+59))/(2)=(30*60)/(2)=900`