Find the sum of the following number sequence: #2+4+6+8+10#?

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Answer 1 · 2016-04-22T06:39:20

30

We'll solve this bit by bit:
#2+4+6+8+10=6+6+8+10#
#=12+8+10#
#=20+10#
#=30#

Answer 2 · 2016-04-22T16:57:58

Sequences like this, where the numbers are spaced equally, have a quick way to sum up.

Add the first and the last term and divide by #2# to get the mean. Then multiply by the number of terms.

#(2+10)/2xx5=12/2xx5=6xx5=30#

For long sequences this is much faster than just adding.
E.g. adding all numbers from #1->100# inclusive:

#(1+100)/2xx100=101/cancel2xx(cancel2xx50)=5050#