How do you find the sum of the arithmetic sequence 2 + 5 + 8 + ... + 56?

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Answer 1 · 2018-04-18T13:27:55

#color(blue)(532)#

The sum of an arithmetic series is given as:

#S_n=n/2(2a+(n-1)d)#

Where:

#bba# is the first term, #bbd# is the common difference and #bbn# is the nth term.

The nth term is given as:

#a+(n-1)d#

We first find the common difference:

#5-2=8-5=3#

We now find the number of terms. We know the last term is #56# and the first term is #2#:

#:.#

#2+(n-1)*3=56#

#(n-1)*3=54#

#n=54/3+1=19#

#:.#

#S_19=19/2(2+(19-1)*3)=19/2(56)=color(blue)(532)#