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

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(1) Answers

mandynorfleet

See that odd number are in a Aritmetic progression with a1 = 1 and r = 2
30th number of sequence is given by:
[latex]a_{30}=a_1+29r\\ \\ a_{30}=1+29*2\\ \\ a_{30}=59[/latex]
Now you can calculate the sun by:
[latex]S_{30}=\frac{30(1+59)}{2}=\frac{30*60}{2}=900[/latex]