Use summation notation to write the following series?

Question

#4 + 7 + 10 + 13 + 16 + 19#

I know how to expand series in summation notation and simplify but I don't know how to do it in reverse.

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Answer 1 · 2018-04-12T02:29:16

#sum_(n=1)^6 3n+1#

The terms are increasing by #3# so look for a pattern that involves #times3#.

#4=3times1+1#
#7=3times2+1#
#10=3times3+1#
...
#19=3times6+1#

So, #4+7+10+13+16+19=sum_(n=1)^6 3n+1#