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Gauss's Problem and Arithmetic Series

Here's a tricky one:

Findthe summation of ( 3 + 2k ) as k goes from 8 to 50

We can find the first term:

a8 = 3 + 2( 8 ) = 19

and the last term:

a50 = 3 + 2( 50 ) = 103

So... we just need n...

How many terms are we adding up?the summation as k goes from 8 to 50

50? NO! ... 50 = 8! ... This is the most common mistake!

NO!