What is the sum of the arithmetic series 2 + 5 + 8 + ... + 56?

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Answer 1 · 2016-03-28T10:35:55

#sum_(n=1)^19(3n-1)=551#

The first term of the corresponding arithmetic sequence is #a=2# and the common difference between successive terms is #d=3#.

Hence the general term may be given by the formula

#(x_n)=a+(n-1)d#

#=2+(n-1)(3)#

#=3n-1#

So we now need to find which term has value #56# so that we know how many terms to sum up to.

#therefore 56=3n-1 => n=57/3=19#

So we thus need to find the sum of the series #sum_(n=1)^19(3n-1)#.

There are 2 formulae applicable :

#=19/2[2(2)+(19-1)(3)]#

#=551#

#=19/2(2+56)#

#=551#