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 :

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

$=551$

$=19/2(2+56)$

$=551$